Given your interests, unless you want to spend a lot of money chartering out, I'd eliminate CDB and SDP from the list. There's very little to do at/near Cold Bay, and Sand Point really doesn't have much tourist infrastructure to speak of. As for wildlife, about the only thing you might be able to see on Popof Island (Sand Point) would be some of the bison that inhabit the back country, but they're very hard to find most of the time. Around Cold Bay, there is a lot of wildlife (including a famous brownie that interrupted my lunch at the Flying Tigers canteen once, by coming in through the kitchen.) However the village itself is beyond bleak.

That leaves the Pribilofs. St. George is (IMO) much more scenic than St. Paul, with a better Russian church, higher cliffs, more foxes and birds, and closer seal rookeries, but there's very little accommodation for tourists (just the old NMFS bunk house, now renamed a "hotel") and AFAIK no food service - you cook your own at the "hotel," having bought it at the village store. You'd also probably want to hire some local with a truck to take you out and about, but it's definitely worth it. Note the weather + strip at STG can make for some exciting approaches and T/Os, and it can get seriously socked in, so only travel if you're very flexible.

Saint Paul has a much better developed tourist infrastructure, with a newish hotel, food service, and on-island transport options. HUGE bird-watching destination, so depending on when you're traveling you might or might not find it easy to get mileage seats.

So I'd pick STG if you have the flexibility and are willing to play it by ear a little, then SNP. Frankly if you want to visit DUT, CDB, KVC, SDP or other towns on the chain, you might want to look at the ferry at some point in the future.

ETA - as for time to visit, I'd pick the dry season. Late summer/early autumn best, best birding in high summer.