I've been to Lisbon once and am planning on returning later this year, so this is a great thread!
The last time I visited, I stayed at what is now the InterContinental, slightly up the hill, across from the park. It was nice, albeit a slight uphill walk when heading back.
Looking at hotel options, I see that Hyatt is now partnered with a small hotel, the Pousada de Lisboa, way down at Praca de Comerico.
It seems these would both be extremes of each end of the main touristy corridor, from what I recall.

Does anyone recommend either of these locations, or am I better off along the main section of Av. da Liberdade, such as the Memmo Principe Real as previously mentioned above?

On my first trip to Lisbon a couple of years ago, I also stayed at the Intercontinental hotel. This past July, I stayed closer to Praca de Comercio. If I were you, I would choose Pousada de Lisboa. I think location-wise, it's easier to walk to most of the places.

Where did you end up staying? Considering a stay at Pousada de Lisboa so curious how it went!

I actually stayed at the Hotel Avendia Palace, right next door to Rossio Station and it was the perfect location. I would say the hotel itself is a bit "meh" but the location couldn't be beat. We were able to walk everywhere and it was pretty centrally located such that there were places/things to explore in all directions. I definitely had a different experience than my first visit where I stayed at the InterContinental (actually its predecessor hotel).

The Rossio area is my favorite place to stay. Yes, it can be touristy but you can avoid doing the touristy things. It's convenient for walking around Lisbon, going to Sintra, and lots of great restaurants/pastry shops within walking distance. The streets above Rossio are quiet because they're one-way tor cars and very narrow, and tend to be more residential, unlike in Chiado or Barrio Alto. I stayed once in Chiado over a weekend and did not appreciate the sheer amount of noise after 1 a.m., or how many people I had to pass trying to sell me drugs. I'll be returning in April for the third year in a row because I love Lisbon so much.

I'm visiting Lisbon with my daughter for the first time in July.

Someone recommended the Sheraton, I'd appreciate opinions! Ideally we're looking for somewhere central with an outdoor pool and the Sheraton seemed to tick the boxes.

The Time Out Market is the same as the Mercado da Ribeira, in Cais do Sodré

I might break out of my loyalty program bonds here, but for the moment, I'm looking at either The Lumiares or Memmo Principe Real as places to stay next summer.

Can anyone compare those two? Prices are about the same.

Are there any non-affiliated hotels in that price range (€300-400/night) that I should be considering?

Like the OP, I like a perfect neighborhood with no tourists :)

First time visitor and it seems like there are three distinct areas where I could use points for our hotel stays (I have plenty for any option so put aside that piece just purely a location question):

1) Hyatt Regency / The Emerald House area

2) The Ivens area

3) Intercontinental / Sheraton Lisboa area

We'll only be there for 3 days so trying to figure out what the best place to use a central base. We haven't figured out exactly what we're doing yet but I assume a mixture of food, walking around, seeing the castle, etc.

My opinion (I've only been to Lisbon once for 5 days)
I would select the Ivens area as it is walkable to the most interesting parts of the city. Downside is the walk back up hill to the hotel.
Second choice for me would be the Emerald House area, as it is near the water and close to the trams which can quickly take you to interesting places.
Last would be the Sheraton area, as it is not all that interesting or easily accessible to other areas.

We stayed at the Fontecruz, which was a nice walk to the other parts of town.
Others may have different (and better) opinions.

My go-to place to stay in Lisbon is here:
https://www.casabalthazarlisbon.com/...-overview.html

All the rooms are quirky and individual (be prepared for stairs, it's not exactly accessible). Get a terrace room /suite with views over Lisbon - fabulous for breakfast or an afternoon / evening tipple.

The breakfasts are the absolute highlight and are just delicious - continental style, with pastries from the renowned Confeitaria Nacional, delivered at a time of your choosing. There's so much we would put left overs in the fridge / cupboard for afternoon snacks!

Its location is within easy walking distance of all the parts of Lisbon I like to visit. Anything else is a short ride on public transport / taxi.

Both are in a touristy neighborhood. If you want no tourists, stay closer to Saldanha.

Thank you! I had the Ivens but we just had to shift our days around and The Ivens is no longer available so for now I'll go with The Emerald House and keep an eye out in case the Ivens opens back up for our new dates

I recommend 1000% Casa Do Barão.

Small, intimate, awesome breakfast, just a little out of the city center. One of the best B&B we ever slept.