good scrambles in and around Jackson/GTNP to maintain fitness

Looking to have an extended stay in Jackson and would like some unfussy hikes/scrambles to maintain fitness and acclimatization in between Grand Teton summit days. An ideal outing would be about 3-4 hours roundtrip, aesthetic, and get some decent elevation gain. Leaning toward scrambles over trails, as the latter are likely to see a lot of traffic during summer. Thanks

There are many, but using distance and elevation as qualifiers rather than time might help folks give you better recommendations.  What some people do in 3-4 hours, others spend literal days on. 

I don't know about 3-4 hrs rt, but a few day trips I've done are pretty nice.  The NW couloir of Nez Perce is class 4 and a bit loose in spots but is a cool view of things. Also the SW couloir of Middle Class 3 is good and the NW couloir of South can be combined in one day for a good day out.  Take an ice ax.  Also have enjoyed the E ridge of Buck Mt. class 4.  Liked it better than the E face which is supposed to be so good and it's fine to down climb without all the snow and loose rock on the E face.  E face of Teewinot is ok but a lot of loose rock about on downsloping slabs and not really one I'd recommend solo.  

Hard to find anything worth a s**t for 3-4 hrs out.  Well, be careful and attentive and don't get so wrapped up in "having to do it or I'm a failure" attitude that you get hurt.  Lots of that over there these days.

Bob gave most of my recommendations.  I never spent time hiking near the town of Jackson, but for the park some of the best "going up" is the Lupine Meadows trail.  It's probably the most efficient trail for conditioning, and is a good run.  Surprise and Amphitheater Lakes are good conditioning hikes, and if you have time continue on to the Teton Glacier under the North Face of the Grand and Mt. Owen.  If you're a trail runner, the whole valley and range is your oyster, however the expansion of grizzly bears increases risks--trail running in grizzly country is likely the best way to come in conflict with bears. 

Not a scramble but the Cascade to Paintbrush loop is stunning. More than four hours unless you run it.

There's a ton of scrambles with short approaches across Jenny Lake worth considering as fitness-keepers. Cube/Ice/Storm point each have scrambles to the summit, going up/down Symmetry Couloir (not my pick for type 1 fun), etc.

Probably worth consulting the Jackson/Ortenburger guide for 4th class routes in that general vicinity. There's relatively short-approach stuff in Hanging Canyon and Death Canyon as well IIRC but from my recollection most would constitute a bigger day (up+over type objectives).