I currently have a Savage .270 and find myself in exactly the same position. I picked it up from a pawn shop for an absolute song but made the mistake of shooting it first. The accuracy is so good I just can't justify tearing it apart yet.
I've gone back and forth on: 6.5-284, 6.5-06, 6.5 PRC/SAUM, fast twist 270 with 170 Berger, 280, 7mm SAUM (or Sherman Max), 7-300 WSM, and 7-300 PRC (I've got about 1000 of the 197 Sierras waiting on a project to use them on). I think I'm pretty down between the 6.5 SAUM, fast twist 270 (maybe as a 270 WSM) and 7 SAUM/Sherman Max.
I've got a Golden Eagle on it and it would really be for long range "benchrest" shooting (although I'd probably shoot it from a bipod and off the ground at my clubs 1000 yard matches) as opposed to hunting.
If this was as a hunting rifle, I'd probably keep it a 270, use 150-170 grain bullets and use it to kill anything with hooves in North America.
if you're looking for more of a target gun, I'm really liking the idea of the Sherman max case and heavy 7mm bullets, but with the slower powders in the 6.5 SAUM, barrel life is supposed to be very good.