Mileage Plus (UA) allows one stopover on a round trip so might be good for this routing (SEA-BJS-xxx-SEA), but the exchange ratio is bad (2 SPG for 1 MP mile). I think that AA is point to point only, no stopover, so you would need three one-way awards, on the other hand the exchange ratio is 1:1. SPG has 30 transfer partners for airline points, and learning which is the best is going to take you some time. Each FFP has its own benefits, drawbacks and quirks.

First think about what is important for you - first, business or economy, are you trying to minimize points usage, want non-stop flights or connections are OK, what dates will you travel and how flexible are you with those dates, how many people are going, etc.

Then the simplest way to solve your problem would be to use an award service. I'd expect that they would already have a decent idea about the various FFPs and what the best way is to accomplish your goal. and I am sure they could help out on this if you want to pay a fee. See thread.
http://www.flyertalk.com/forum/trave...e-reviews.html