I was in a similar boat about 4 years ago when I got my Marriott LT Plat status. I went with Starwood as my 2nd choice (and Priority Club as my 3rd choice which I'll talk to in a moment.)
If I were making the choice today AND Hyatt has hotels where you will be mostly staying, I would probably go with them. Their program is basically the best of Marriott's, Hilton's, and Starwood's all rolled together. As you note, though, in terms of hotel locations, they need to percolate a bit more. But they probably offer more than the others due to their limited number of locations. (I think Starwood has gone through the exact same cycle. As they have grown, their benefits get closer to their main competitor's.) So if there are Hyatt's around, I suspect they will meet more of your requirements than the others.
Personally, I didn't really focus much on Hilton as they are the closest program in terms of hotels and benefits to Marriott. I wanted to try something a bit different and thus Starwood was my choice. Note that I had never been Plat with them before, so I was able to get a Plat status match. You stated that you didn't really think much of IC hotels due to there being a Marriott close by. Well, I don't think there is a hotel chain more like Marriott than Hilton. Yes, there are differences, but overall in terms of locations and the program itself, Hilton has a lot in common with Marriott.
The Ambassador program with ICH may be a good option as well. If you travel enough (and stay at ICs enough) to get RA status, you may find that is the best top level out there in terms of pure elite benefits. You'll get your upgrades, you'll get free access to the room mini-bar, you'll get your lounge access, etc. But, their hotels outside of ICs can quite often leave something to be desired and your elite recognition will more often than not be minimal (though I have received lounge access at every CP I've stayed at that has one.)
Now with that said, I would (and do) use Priority Club as a 3rd choice for some easy points and stays at out of the way places that can be hard to find the other hotel chains. It is very easy to maintain Plat status (i.e. just get 60K points/yr.) And if you need one night at a small airport somewhere, or some small town, you'll most likely be able to find a hotel there where you can use points. I plan a group's stay at a conference in January of each year (20 rooms for 2 nights) and that gets me my 60K points by itself. You could also churn the PC branded CC yearly (it has a 60K sign-up bonus).
If Hyatt's locations don't work for you, I think even though you might have to "suffer" a bit at Starwood hotels until you get Plat status, it may still be one of your better options. There are probably some ways you can get at least Gold with Starwood and you can stack up to 2 CCs for the nights/stay credit. Since you have mostly one-night stays, if you have get the 4 stay credits from the CCs, you will only need 21 more stays (nights) to get Plat. And by the time you are ready to take one of those vacations, you should have your Plat status wrapped up and be able to stay in luxury all over Europe.