How about a Build-a-Bear party (If you have one local to you)? My niece went to one recently & loved it!
I have been looking into the same thing, although like Joolz, it is a fair way to the nearest one and the kids will spend double the time in the car that they will at the party. I was googling ideas a few weeks ago and did come up with this
http://www.childrensartparties.co.uk/?gclid=CLf8-vu_kqYCFQJO4QodyUqrZw#/party-options/4534334983
I think you do need to host it at home, but my issue with parties at home is you become the caterer, entertainer, DJ and the cleaner. I do like the idea of them sending the things out to you. Not sure what kind of space you have though and how many you were thinking of inviting. If there are quite a few then it will blow your budget anyhow.
Honestly, despite the hassle, when it comes to budget the most cost effective way to do it is to keep it small and do it at home. DD had a huge party last year, hired a hall, entertainment etc - there were 30 kids and it cost a fortune. The previous year I had done a Tiaras and Pizza party at home for 5 girls. They really entertained themselves a good part of the time with DD's toys and things.
All I did was issue each princess with a tiara and a wand when they arrived and they each got a "Royal Fruit Plate" which was fresh fruit arranged on a gold paper plate. I did some party games for them and did a treasure hunt later on. They don't really have expectations at that age. If there are some games, prizes, a party bag and cake they are happy. With the pizza I bought mini margarita ones and had an assortment of chopped toppings for them to do their own. While it was cooking they got to decorate a cookie for dessert.
DD is also a Feb birthday so keep your eyes open now for clearance gifts and nik naks for party bags.