2015 Honda Accord with roughly 50K miles. I had new tires put on two weeks ago because they were terribly worn. The tire shop said the tires showed signs of very bad alignment. So a few days after the new tires were put on, I took it to a local shop for alignment. The next day I drove on several roads (including a highway). I noticed two things:

1) The steering wheel had to be turned slightly to the left (maybe a couple of degrees) in order to go straight.
2) If I let go of the steering wheel for a while, the car would eventually go to the right.

Reported this info the local shop, and they claimed to "tighten up some bolts" and that their instruments showed it was in perfect alignment. However, I still notice the exact same behavior.

Should I have the alignment checked at another shop? Or does this sound like normal behavior?

 

Something doesn't sound right. The shop might have aligned the tires perfectly, but the steering wheel could have been off a few degrees. This is something they should be able to easily fix.

The eventually turning right may be due to a slight grade on your road. I'd take the car back to the original shop and have them adjust the alignment with the steering wheel pointed straight, since you paid them originally to do the work.

 

This^^^. Try the eventual turning test on a straight interstate highway since those are flat. Watch for crosswind effect.
I run my tires with pressures some 2 psi above car recommended pressures, usually labelled on door jam, you might try that also. Tire pressure gauges are $4 in any auto parts store, measure pressure in AM before driving..