Staying in Europe for three months

Where have you been before in Europe? I would suggesting going to another region.
And I would suggest going to completely different ends of Europe. Budget airlines can get you anywhere for $100 or so.
How about Budapest in an apartment (Paty's Place) and taking excursions into the countryside. It is less expensive than other cities. Then fly Wizz Air to Lisbon, Portugal. Then TAP Air Portugal to Copenhagen.
I still have not made it to Dresden and the Saxon mountains over on the Czech Republic border. We are taking in SW Ireland via rental car next month. There is a lot to see there.

I have been to San Sebastion, Madrid, Sevelle, Granada Spain, and to Italy on Rick Steves Heart of Italy tour.

Thank you for your input as I will consider all options.

guessing you will be going in spring/summer?
three months or 6 weeks?
you might find two weeks in one city a bit of a waste? with so much to see. depends on what type of holiday you are after?
once you have looked around for even a week in a large city they can be a bit much, and expensive. that said.
we have been to a very large number of cities/areas in europe and we generally keep going back to anywhere near the alps. ie: north of say milan, east of geneva, south of munich, west of vienna. spectacular scenery, very modest prices ( except Switzerland) lovely small towns and not too busy . austria is very underrated.
there are plenty of opportunities to stay in a small pension, B&B etc meet 'real' people and see local things.
just get past the mind set of staying in hotels in big cities and stay with someone who can suggest local things to see and do.
while is not everyones cup of tea, we enjoy combining these options with also seeing larger cities in the one trip. thats the advantage of taking a longer time. ( we go for 2 months at a time)
hope this helps.

If you're planning to stay for three months, one important point to note is that you must limit your stay to 90 days, which includes your arrival and departure days. This is required under the terms of the Schengen Visa, which limits tourists to 90 days in any 180 day period.

I suppose you could start with which countries / cities interest you the most?

With the length of time that you have, I would consider alternating cities and more rural areas. For instance, 4 days in Paris, 4 days in Chartres, perhaps going to Normandy or Bretagne. In many rural areas, hotels are much more reasonable, food costs are lower, and you get a much more up-close contact to ordinary people. Perhaps in Germany, some time in Munich, some in Nuremberg. Then moving to Leipzig-Dresden-Erfurt and small cities.

But really you need to do a little homework, and provide an outline of what you are thinking about. What countries? What regions? There are 200 cities in Europe that I would love to visit.

We spent two weeks in London last year and it was our best visit yet, in fact, our fourth to that city.

A week or two in Paris would not go amiss. The same for Venice, Florence, and Rome. All of these offer endless things to see and do plus ample day trips opportunities.

I'd add Berlin and Barcelona to the long-stay list. But I wouldn't want to spend 90 days just moving from one large city to another, even allowing for some day-trips.

With the idea of 1-2 weeks in one place, I'm surprised that there's been only one mentioning of the option of renting an apartment.

The major listing resources are HomeAway, VRBO (vacation rentals by owner) and Airbnb. Many cities and towns will have local listing sources as well.

Of the ones that cover many locations, I prefer Booking.com. You can limit to apartments as well as in a number of other ways. Keep in mind that there is no star system for apartments. I think it's better for any kind of lodging to filter by review score. When I look there I only consider places with a score of 8 or higher.

We frequently stay in Europe for periods of 5 - 9 weeks at a time usually basing ourselves in either 2 or 3 places. We have found that the bigger the city the better time we have. Our pattern tends to be that we start with the things that are closest to us and spiral further and further out until we have exhausted just about everything in the area, well known and NOT so well known! As we go we find out about places from local people and also just happen upon places because we can take our time and to explore. Our favorite places have been, along with length of time we have stayed, are Paris (5 weeks), London (5 weeks), Prague (5 weeks), Alesund, Norway (4 weeks), Pezenas, France (5 weeks), La Tzoumaz, Switzerland (4 weeks). This week we're headed back to Paris for 4 weeks - still haven't exhausted everything there is to do there! There are a few other places we've spent time in where we ran out of things to do...they were quite rural though and you probably wouldn't end up in any of them. Just make sure that your expectations are realistic...you cannot possibly fill up every day with activities. We often spend the morning seeing the sights or visiting landmarks. In the afternoon we'll relax, then go out for dinner and walk around after dark. In more rural locations we spend a lot of time walking and hiking, which we love to do. Just make sure that wherever you go you has the kinds of activities you enjoy doing - we once ended up on an island and started to lose our minds after about 2 weeks. Won't make that mistake again!

Lo is right, in case you havenàt thought about it: Apartments are essential (IMO) for long stays. We use apartments when we stay 4-or-more nights, which is almost always. We do not like eating in restaurants every night for weeks on end.

If you want a more rural experience but no need to rent a car, try Lauterbrunnen in Switzerland for a couple of weeks. With a Berner Oberland Regional Pass you can take many day trips or simply hike in and around the valley.

I also tend to get bored for over a week in the same place, even if it’s a large city, however some locations, like Tuscany, offer tons of day trip opportunities, which can easily keep you busy for longer than a week.

Where to base yourselves for each week or two depends also on whether you will have a car or not.
Let’s say you intend to spend two or even three weeks in Tuscany. With a car I would probably stay in a country house or hotel, or in a small town. But without a car, if you want to take advantage of the many day trip opportunities, you need to stay in a public transportation hub like Florence (or maybe split 7- 10 days in Florence and up to a week in Siena, which is good as a base for that part of Tuscany).