Huh? The only place near LAX that the Big Blue Bus goes is to the LAX bus station, which is not in the same area as the rental cars and a few parking lots away from all the hotels (and facing the backs of those hotels, so even more blocks to walk around to the front).

Avis is a couple blocks away from the 4 Points, a few blocks further from the Sheraton Gateway. The Westin is way way further (another half mile or so). The other rentals cars are progressively further away by multiple giant blocks, with Enterprise being a miles or two away! There may be one other rental car company about as close as Avis, I forget. (I know it's not Hertz, that one's a long block or two further away.)

Similarly, the 4 Points is closest to the airport bus stop (but still about half a mile away, in a different direction that the rental car places), and again the Sherton Gateway is several blocks more.

Now, if you have time to kill, what you could do is take the rental car shuttle to the airport, and then take the hotel shuttle from the airport. And take the airport shuttle bus to/from the airport when you want to transfer to the Big Blue Bus. That takes a bunch of extra time (but I don't know how much longer time than walking many eternal giant blocks of parking lots), but it does free you up to stay at any hotel which has an airport shuttle.

But supermarkets??? Forget it, all of the places around the airport that are close to the bus station and close to the rental cars are far from where most ordinary people live. The supermarkets are in completely different neighborhoods. The best you'll find is maybe a convenience store. Restuarants, other than the ones in the hotels and at the airport, are spotty too. However, there's a handy strip club! (Ie, the area all around the airport is extremely industrial, with all the implications of that.)

Now, what you could do is return your car, shlep somehow over to the bus station, and take the Big Blue Bus back to Santa Monica, stay there, and you'll be close to everything (supermarkets, restuarants, and real non-industrial life!). Except the airport, that is. So you'll have to take the Big Blue Bus back to the airport (transfering at the airport bus station to the airport shuttle bus).

If there's an area where you can stay near LAX (at an SPG hotel or otherwise) where you'd have both an airport shuttle and a supermarket within walking distance, I don't know where that would be, but you'd definitely no longer be anywhere near the Big Blue Bus station.

FYI: The Big Blue Bus is Santa Monica based, and only one BBB line goes out to the airport. And Santa Monica (and thus the one BBB line that goes to the airport) is northwest of the airport, but the airport SPG hotels are either East or due North of the airport. So none of the SPG hotels further away than the 4 Points / Sheraton Gateway are anywhere close to a Big Blue Bus line, until you get to Santa Monica itself.

As far as hotel hopping, it's reasonable between the 4 Points and Sherton Gateway without a car, but not reasonable without a car between any other pair (unless you want to take one hotel shuttle to the airport and the other away from it, or unless you can convince the hotel shuttle to take you from one SPG hotel to the next).