Hi Jenness0429. First, I thought you might be interested in reading a thread I started about the piazza that you were adjacent to when you were in Rome last. (I posted it on Slowtravel, where my name is "Jady"):
Rome's Piazza San Silvestro got a makeover

Regarding the name of the area you're looking for - it could be called many things depending on the booking engine, or hotel's marketing choice. Downtown Rome, historic center, centro storico, Spanish Steps area, Trevi Fountain area (or its Italian names for these last two of course)...

This is how I look for accommodations when I have a specific area in mind: I use google maps as the starting point and look for the imbedded ads for the various hotels and accommodations, then click on the hotel's website to gauge the prices and how the rooms look, and then if that passes muster I look at TripAdvisor for the reviews. If the reviews are good, I then go back to the hotel's site and try a dummy booking for the dates I'm interested in to see if the rates are affordable.

And I did just that after plugging in the address of your first hotel, The San Silvestro, and the third place I found looks extremely promising, in fact I've just bookmarked it for my own files. And it turns out, it's the first one mentioned in your list above. (About the others on your list, I only know what the online reviews say, I've never stayed at any of those places myself).

I looked at your other thread and see you and your husband need 3 nights, mid October and above I see your requirement of a $300 - $350 price. Guesstimating a $1.35 conversion rate (incl the FOREX your cc will charge), that means you're looking to spend €220 - €260. And that you want something "nicer" than the San Silvestro.

If you want a full service hotel, with nice public spaces (lobby/bar), a staffed concierge desk, bell hops, etc, then my suggestion is not for you.

But if your definition of "nicer" just regards the room itself then my suggestion may be something for you to investigate.

Suite Della Vite

Regarding its location, here you see on Google the proximity of this to your San Silvestro (Hotel San Silvestro is marked 'A', Suite Della Vite is marked 'B').

This is not a "hotel" though in the conventional sense. From what I've read, it seems this a relatively new enterprise by the restaurant owner of the adjacent Ristorante Mario. It appears to be comprised of only 3 individual accommodations: a classically decorated 25 square meter (270 sq feet) classic studio, a similarly decorated 45 square meter (485 sq ft) deluxe studio and an ultra modern and sleekly decorated 100 square meter (1,075 sq ft) penthouse. And that as a fourth choice, there are rates to rent both studios together which appear to connect via an independent foyer. However, the wording on the website implies there is more than 1 deluxe studio - but my gut is telling me that there are only 3 units in total, FWIW! [Note, I converted the square meters myself - the website shows inaccurate conversions to square feet). The description of the penthouse is that it's comprised of 2 levels on the 6th and the 7th floors, but there's no mention what floor the 2 studios are on. So our restaurateur has converted some apartments in the adjoining building and opened a "hotel". And in the reviews I see that you need to go into the restaurant to "check in" and from there you'll be escorted to the apartment. Here's the google streetview of the apartment building, number 54, seen between the awnings showing Ristorante Mario.

You're probably wondering why am I excited about this odd place?! I first am impressed with the size of the deluxe studio, 45 sqm. This is very spacious for Rome. I'm next impressed with the quality of the furnishings and the bathroom, and that is has a kitchenette. It also says you get bathrobes and slippers (to me, always a sign of a "nicer" place), it's soundproofed and you're gifted with a bottle of wine on arrival. From the website:
And next I'm excited about the price. I plugged in random dates for October and received a consistent €250 for Sunday thru Thursday nights, and €280 for Friday and Saturday nights. And these rates didn't change if I entered in 1 guest, 2 guests, 3 or even 4 guests. And the rates include breakfast.

And the reviews are very good overall.

So to me, based on its locations, the price, and the quality and size of the room makes me feel comfortable recommending it to a friend - providing they were already familiar with Rome somewhat and were comfortable being in an independent environment. I also really like that it has a kitchenette. For longer stays than yours, this could be extremely handy. Of course, this brings up the question of, what not just rent an apartment? And you could find one, much cheaper than this - but you'd have to in most cases prepay a deposit, that very well may not be refundable, and you'd most likely have to pay the balance in cash upon arrival. This place though, IS set up like a hotel in terms of its booking policy. Your cc is only used to guarantee the res, you can cancel without penalty up to 2 days prior to arrival, and if cancelling within 2 days, you're penalized the first night's rate (and all that is very standard).

I'm also bookmarking this for future use because its 100 sqm penthouse seems amazing and its rates, again with random October dates input, are €380 for Sun - Thurs and €440 for Fri and Sat. And these are the same rates if you were to rent the 2 studios combined. These prices are comparable to a standard room at many luxury hotels in high season, which usually would only be about 35sqm. (But of course, for those hotels you'd get a "real" hotel).

Here's the hotel's website:
http://www.suitedellavite.it/homepage.html

Here's the page describing the Deluxe Studio (I most like that they include a floorplan for each room):
http://www.suitedellavite.it/studio-brunello.html

Note on the website: As you look at each room category's page you see pictures flashing above, but these are not necessarily the pictures for the room type in question. For that click on the pictures at the bottom of the page. And I noticed that the pictures shown for the Deluxe Studio include a shot of 2 different bathrooms - so one of those pix must go with the Classic Studio. And the pix shown in the gallery on the Classic Studio shows the picture for the Deluxe Studio. But since floorplans are also shown, you can sort all this out for yourself. And there's also an offer for a discount to his restaurant.

Here are the Tripadvisor reviews (there are not many, which would make sense since this place is fairly new, so do use the Google translate feature to learn from all of the reviews):
http://www.tripadvisor.com/Hotel_Rev...ome_Lazio.html

And here are a couple more reviews through Expedia:
http://www.expedia.com/Rome-Hotels-G...m1=a2&#reviews

And Venere only shows one English language review:
http://www.venere.com/inns/rome/inn-...-vite/#reviews
And one in Italian:
http://www.venere.com/it/pensioni/ro...-vite/#reviews

Jenness, this place seems to meet your location and price requirement, but whether you'd be content with basically renting an apartment, vs a hotel room is the question. If I was planning to book this for a friend, I'd probably email the "hotel" and ask what floor the studios were on, and where the windows faced (the street or an interior courtyard) and I'd ask if there were more than one Deluxe Studio and more than one Classic Studio. Maybe this guy owns a few floors of the apartment building and there are more than 3 units?! And I'd ask this because IF there is more than one Deluxe Studio I'd want to make sure that the pictures I was seeing online correspond to the room that I'd receive. And if you do email him Jenness, I'd let him know of your profession - I'd imagine he'd be interested and would perhaps extend you more favored treatment if you were to dine in his restaurant or at the least, take more care in the bottle of wine he selects for you....

And lastly(!) I apologize for the rambling and ridiculous length of this post, if I was a professional travel agent I would have taken the time to edit and condense this - but I'm just a fellow traveler who happens to be fairly obsessed with Rome.