My number one recommendation would be the Polynesian - but it may be more than the $150 per night. Check on a garden view room.....
It is very quiet and relaxing, with huge rooms and an absolutely GREAT location.
Of the choices you mentioned --- I have stayed at all except Swan. (PO RIverside was Dixie Landings then - same resort, just a name change.)
Let me think: AKL is wonderful! It is quite and relaxing and the animals and African art and storytellers are great. The resort is somewhat dark and that makes it even more relaxing. That being said, it is the fartherest away from MK, EPCOT and MGM. And the only mode of transportation is bus. The buses are solely for AKL (no sharing with other resorts). And even the MK ride isn't very long (10-15 minutes? maybe longer if crowded). And the rooms are not very large. So my recommendation: very relaxing, you will REALLY feel like you are getting away from it all; but you will have smaller rooms and a longer ride to the parks. There may be a running trail, but I don't remember it.
Dolphin - Swan. We liked the Dolphin and the room was larger than AKL. But the place is HUGE!!! It felt like we were a long way from EVERYTHING. Swan is much smaller and that would probably make it better. The earlier poster was right that it just didn't have that "Disney Feel" and we won't stay there again. But the location is very good (Beach CLub is better for EPCOT, Yacht CLub and Boardwalk is just as good and I think I would like both better than the Dolphin. Boarwalk & Swan would be a littler closer to MGM - but that is pretty much a tie. For MK: Poly, Contempory and GF is better.) My recommendation: not very relaxing - more of a fun family atmosphere - and a rather long walk to everything (Dolphin). Can't argue with the location or the cost; rooms larger than AKL, but still not all that large - no where near as large as Poly.
Port Orleans - very relaxing, but back to only buses for transporation. Riverside is very spread out - so you risk being very far from the main hall. But it is a beautiful resort - the grounds are lovely. The room is not very large - it didn't seem any larger than the all-stars..... We did not like this resort. We were 4 miles (it seemed) from the restuarant and main pool. We had stayed in the all-stars earlier and couldn't figure out what we were paying extra for here. The buses make 5- or 6 stops and that gets really annoying after awhile. I think the PO French Quarter would be much preferable to the Riverside part.
SO! Still my number one recommendation for what you've said you want is the Poly (except I'm not sure on the cost). But of the ones you mentioned I think I would recommend either AKL, PO French Quarter or the Swan (I wouldn't stay at the Swan because I would miss the Disney feel of it, but many others do not feel that way at all).
I cannot recommend PO Riverside or the Dolphin for you.
Check out these website to help get you more information
Deb Willis' Disney Site
Tikkiman's Poly Site
I almost forgot: there is a running trail at both Swan/Dolphin and at Port Orleans.