Since the request is extremely vague and general, and lacks a lot of useful detail (such as budget, preferences, etc), I can offer some equally general, but hopefully helpful suggestions.
Amusement Parks - ie Disney, Legoland, etc.
Beach destinations - Take your pick based on budget and other preferences. Most kids love the beach. They will play in the sand, play in the surf, pick seashells, swim. Your child is old enough to accompany you to do things you want, but she would probably prefer to just stay on the beach all day, every day. We did this recently for 5 days in Vietnam. You should obviously pick a place with weather appropriate for the beach for the month you are travelling.
Somewhere with snow - Similar to beaches, most kids also love snow. Skiing, sledding, or just romping about in the snow.
4 is actually a decent age for a young traveller. I was toting around a 1 year old when my oldest was 4, so we had to cater to the little one, but my 4 year old was very easy to manage. I would say almost anywhere is doable with a 4 year old, but if you want her to be happiest, stick to things she will enjoy rather than things you might want to do.
If you MUST choose an urban destination, look for one with lots of parks and children's activities to visit, such as aquariums, science museums, zoos, amusement parks, etc. and then space out your activities with hers.