If you read the posts here you might notice that I am somewhat biased. But you will also note that I rarely respond to a “where should I go” question. You however have struck a chord where I think my bias can put into proper perspective. Like you I enjoy Paris immensely, like its reputation suggests Paris is a city to be lived; not visited. Prague is more a great place to visit which is why maybe it did not have the same impact on you. Another great city that is best served if you live it is Budapest.
Budapest is called the Paris of the East for a good reason. Budapest is sort of a Paris in the midst of being restored. It’s a little rough around the edges but that only serves to make it more real. Like Paris it has a distinct culture and a love of the arts. And like Paris (and unlike places like Prague and to a lesser degree Vienna) you don’t go to see a Tourist District you go to experience the various zones and live within the culture.
Safety? Budapest always ranks as one of the safest cities in Europe. The first few times we went we were amazed to see young ladies walking home alone after dark had set in. Later through local friends and a little internet research we discovered just how safe the place really was. We generally stay in a ground level street facing apartment and we have absolutely no concerns; beyond a little common sense I guess.
If you love Paris I think Budapest will speak to you in many similar ways. Get a well located place to stay, spend at least four full days. Some sort of self-catering arrangement would be an excellent idea. A place where you are forced a little into the daily life of Budapest by having to do a little grocery shopping. The Markets are wonderful. Possibly take a cooking class while you are there. Then there are the theaters and concerts (but come early in June because like much of Europe much closes by mid-June).
The transportation in Budapest is part of the attraction and character of the city; especially the yellow trams and the almost Mario Brothers like M1 Metro Line (the oldest on the continent of Europe). You will find the metro system extremely easy and extremely affordable. Even the weather curiously enough is very similar to Paris. If you look at all the averages for both cities there are very few differences.
But you have three weeks, so where else? Vienna is a natural and some of the smaller towns between Vienna and Budapest you might find interesting. By working Vienna and Budapest and either Pecs or Salzburg as three hubs you will see more and spend less time traveling. If you are brave head for Bulgaria or Romania; two other places I love dearly. I love the region and can help if you are interested.