Also worth noting with these suggestions is Philly is a little less than 1.5 hour train ride to New York City, Washington, DC is 3–4 hour train ride to New York City (depending on whether you take a fast train), Boston is about a 4 hour train ride to New York City. So, there are many major cities easily visited when you live in that northeastern part of the country. Also, from all these cities there are many many flights at reasonable fares to FL for a quick vacation.
But, I don’t mean to discourage you from cities like San Francisco, which many people have suggested.
Seattle is very close to the Canadian Border, and just a short distance away is Vancouver, BC, Canada, which is one of my most favorite cities to visit. Big negative for me about Seattle is they have many days of overcast weather, but for people from the UK it might feel quite nornal.
I have never been to Denver, but most people I know love it there, if you like the mountains and to ski that might be ideal? They have 300 days of sunshine per year even though they get a lot of snow in the winter.
America is so huge. Your question is similar to an American asking what city in Europe would you recommend? Our country is almost as big as Europe in total. What would you pick? Milan, Rome, Berlin, London, Glasgow, Barcelona, Oslo, Paris, so many choices. I don’t expect you to answer, I am just pointing out that sometimes people outside of the US think of us as a single country with the refernce point of their own country. But, most other countries are much much smaller. I am not assuming that is the case her, but wanted to point it out.