You didn't get the memo? EU annexed it last week because they all wanted SodaStream units.
I totally didn't even read who the OP was when I commented, my bad, but my list still stands in general.

s'Hertogenbosch or Utrecht

Barcelona - More "modern" but more than enough to "see" and substantial ease in doing so. I suspect that Barcelona might be a one time choice, "once around the track" enough, but I can think of no more appealing city for a first and serious visit.

Oxford and environs - One of the best "one week' vacations we've ever spent was in Oxford, with several days of car rental to visit some nearby sites/attractions.

Bruges - a week may be more than needed, but allows for a couple of days in a nearby city such as Brussels or other short side trips.

Lisbon - an easy choice

Istanbul - on the edge, but European enough to qualify. It's been a long time, but it tops my list to revisit soon, even with some social and political discord.

In any case, get yourself out of the big "branded" hotels. We used to stay on "points" often, and I recall the awful realization one morning at Vienna's Marriott at the Spanish Riding School that, even with Vienna's great charm and character and the staff's accents, I might have been in Kansas City. Unlike the US, Europe has hundreds (no, thousands) of appealing small essentially "owner-operated" hotels, many modest in features and facilities (and a week with a tiny bathroom will not spoil your life), but which for a variety of reasons provide greater access to local culture, venues and activities. Reviews for "non-resort" hotels of this sort are easy to "filter", and even the negative reviews may subtly reveal good reasons to select one.

Edinburgh or Dublin.

Mmmm. Tenements. Yaaaay.

One of these for a whole week? Yikes that would get boring.

From Edinburgh, I would suggest taking a side trip by train to York. It's charming but much too small for a week.

Of course! Have you never seen Eurovision or the Europa Cup?

Liverpool and Manchester is as 19th century as it gets - They both rose to world prominence at that time. Both surprisingly interesting, lots to see, good value, and easy to reach.

Barcelona is one of my favorites.

I'd say that Barcelona would indeed be a grand choice for you -one of my favourite places in Europe to visit.

It's also in the Asia-Pacific region, according to Fifa.

Since you mentioned Eurovision, how soon until Azerbaijan makes it into the EU? Heh...

A quick review of the cities mentioned:

Lisbon: At age 68, hills are a problem. That's why I now avoid Rome.
Porto: I know nothing about it.
Barcelona: Good possibility.
Istanbul: I've been there twice, but since Erdogan outlawed gambling it has lost much of its attraction for me.
Amsterdam: Another good possibility.
Tel Aviv: Besides the fact that I go there several times each year, I actually find it a boring city -- but I would love it if I were in my 20's or 30's.
Dubrovnik: Good possibility.
Talinn: I have never even heard of it.
Krakow: I will probably be going in early May, and Poland might still be freezing.
Belgrade: Good possibility.
Brussels: I have been there and found it just "so so".
Antwerp: I know very little about it.
Ghent: See above.
Sofia: For some reason, I like the idea but I am not sure of why.
St Petersburg: See remarks about Poland.
Valencia: Possible.
Toulouse: It is borderline -- I have never been there but have spent a lot of time in France.
Nice/Cannes: Been there, done that, got the t-shirt.
Copenhagen, Stockholm, Oslo, Bergen: Not before the summer.
Salzberg: Possible.
Vienna: Possible
Birmingham, Glasgow, Leeds, Oxford, Edinburgh, Liverpool, Manchester -- I think I will pass on the UK. Its not very European.
Bucharest: Possible.
s'Hertogenbosch: Possible.
Utrecht: Possible.
Dublin: See comments on the UK.

As Vienna is a possible let me give a mix. Spend a few days there and then venture over to Bratislava which is one hour away and spend a few days there.

Antwerp/Bruges/Ghent would also make for a nice week.

I like Barcelona but damn last time we were there in late September it was over run by tourists. Painfully over run. We found Sevilla to be much reasonable. And would combine with Cordoba/Granada. Madrid is also reasonable.

"Sofia" is likely the name of an old girlfriend.