DH and I not big travellers , but want to do 2 weeks abroad with DD who will be 4 next Jan and we want to go in June and make the most of our last cheaper holiday!
We like walking, looking at historic things, swimming, nature and spending time together . Therefore, we don't know how we feel about a AI resort although we like the idea of not having to cook for ourselves and the prospect of some children's activities so we can get some time for ourselves occasionally . 
In terms of location, we looked at the Italian lakes but all the hotels seem so dated (but this could be a European thing as I recall a lot of hotels in France being like this when I last went!) and expensive.
Ideally we want short haul and not to have to book a car, but I have no idea where to start, Budget is £3-4k. Will not consider camping!, but might be happy with a villa on a resort or a hotel. Any suggestions gratefully received! TIA