I bet I know exactly which trail you're talking about. Was it along the Snake river out in the flats? I used to always carry a laptop running Street Atlas USA on trips and I've kept all my GPS logs since 1999 so I could look at them later for times like this. I now use A Garmin Nuvi 2757 with 7" display but I also keep its logs.
Coming back home from Jasper, AB in June 2005 we took a very cool trail, just north out of Jackson but south of Jenny Lake off of the Teton Park road. It was very cool and it followed the top of the bank of the Snake river. We watched a pack of wolves try to take down a bison for several hours until it was nearly dark. Very cool trail and it's called Cottonwood Creek road. The main highway between Jackson and Yellowstone is 191/189. If you're on that road and you're looking West at the Tetons like everyone else, there is a river bank trail on top of the opposite shore line of the Snake river.
This trail makes a loop from Jackson Lake to just south of Jenny lake and follows the Snake river. A stock 4Runner can do it. If there's snow or heavy rain, I'd probably stay off. It's about ~9 to 10 miles total length. It's not difficult at all. Note, I would recommend a 1/2 tank of gas before starting this trail.
(I strongly recommend having GPS when taking any first time trail)
To get there enter Cotton Creek Road at the south end of Jackson lake (N43.823, W110.61498) and you'll come out 1/2 way between Moose and Jenny lake (N43.69919, W110.72681).
If you have Garmin BaseCamp it's also shown as Bar B C Ranch road.
[MENTION=105168]uptheirons[/MENTION], you have easy access to one of our favorite places in the world, Jasper, AB. We love it and have watched the Columbia Glacier recede dramatically in 25 years of visits.
One caution, the higher mountain passes around Yellowstone may still have some snow issues in April. Yellowstone averages 48° to 16° in April. Also check out the park facilities opening dates here.
Opening & Closing Dates of Facilities - Yellowstone National Park (U.S. National Park Service)
Enjoy your trip!