The least hassle for both guest parents and for you, combined with the most fun for the kids is either the bounce place or the indoor mini golf. I voted bounce place because mini golf can be frustrating for 4 y/o kids, but everyone can enjoy bouncing.
At age 4, a party needs to keep the kids moving - so the bounce house or gymnastics or anything along those lines. Arts and crafts type parties are hard - my younger DD went to one and even with 3 different craft stations and lots of getting the kids from one station to the next, some of the kids had a really hard time listening and paying attention - they just wanted to be playing with their friends. My older DD went to a 5th party at a paint the pottery type place and it was horrible for all the kids and parents - just too young for that type of stuff. Bowling can be OK if you have a small group and a lot of adults to help the kids. Older DD has been to a few bowling parties for 5 and 6 year olds and the younger kids always had a hard time and lost interest before they even finished 1 game and they had to have an adult at every lane to help the kids. I think bowling parties can be fun if you have enough adults to help and other things going on to keep the kids busy/entertained when its not their turn to bowl. Older DD was at a skyzone party in the spring, right when she was 6. Most of the kids seemed to love it but I would only consider it if they have a blocked off toddler area and have set things planned to do with the kids for part of the time. The 5/6 year olds at this party were so tired and sweaty by the end. My DD liked it but wasn't interested in going back.
Re: what type of bday party would be best?
bounce house for sure, but its expensive and they hustle your though.
DD's bday is in December and I am seriously thinkign of having a Chuck E. Cheese party.