How much space should at least be around a kitchen island?
Ideally, there should be enough room for a person to get by while there is someone standing at the island working.
So enough room for two people to stand side by side across the gap or pass comfortably. If you have to cater for people with mobility problems you will probably need to make this gap wider to accommodate the extra width and lack of flexibility of someone using a wheelchair or walking frame.
However, depending on your design you might be able to get away with less - especially if there's going to be little to no traffic in that area.
A good way to figure out what works for you may be to find a box roughly the same size as the island (or cobble together something out of scrap plywood and 2x4's) and see how it 'feels'. Stand at the 'island' and have someone open the kitchen drawers behind you, walk through the kitchen and notice if you have to slow down because you feel like you're going to clip the island, etc. etc.
If you're worried about resale, consider your own body size as well. If you've got a small frame, someone larger may not be comfortable with a space that you feel fine in.
42" is my personal requirement. Can't comment on hard requirements with code or your municipality. 36" get crowded too fast in my opinion. 48" is great, but few people have room for that. 42" seems to be happy medium.
If I had a cooktop on there, i might be leary of the 42 depending on how close the cooktop is to the island edges.
Approximately 3 feet on each side is a good place to start.
I normally shoot for 36" min and ideally up to 48" if space allows. Disclaimer: I'm a kitchen designer.
I had a great kitchen with 32 inches clearance and it was fine for a small kitchen.