The Suitsupply in-house tailoring is quite good (as it should be since they are working on the same handful of models everyday and know how they are constructed). However, as with all affordable menswear, the pinning is done by the sales associates—who are often inexperienced are really only look at trouser and sleeve length. You have to ask them to take out the neck roll, narrow the sleeves or taper the torso, etc., as they usually won’t suggest it.
On the other hand, finding an alterations tailor with the chops to suggest a lot of micro-alterations to make a jacket fit perfectly is not easy. If you know what your want, Suitsupply in-house is a good choice.
Not US-based, but I can strongly recommend the services provided in the SuSu store in Brussels. Great service and they've got a dedicated guy to their MTM-service who's very good and attentive.