The W is over next to the Amtrak so a bit of a hike from the Gaslamp. I'd say at least 7-8 blocks. That doesn't sound like far, but it's not in the heart of things for sure.
The US Grant IME can be really good or really bad. The last time I stayed there I had very pushy housekeeping despite me having a late checkout. The front desk staff also seemed very bothered to help me.
In 3 other times there the staff was great. Housekeeping respected the DND and late checkout and I got nice upgrades. Still the bad taste of the last experience is what sticks with me.
I am in the minority but I like the Westin Gaslamp. I got a killer upgrade there to a bilevel suite last time I visited. The staff is always accommodating and the location right in Horton Plaza is great. It's just far enough from the Gaslamp to not be noisy but close enough that you won't mind the short walk.
My biggest complaint about downtown San Diego of late is the pedicab pushiness. It seems worse at the Gaslamp than other hotels. Those guys are everywhere and you're constantly being pressed to take a ride. I wish the city would crack down on that because it didn't use to be that way. I like walking in San Diego and I just want to be left alone.
There are 2 other hotels in the downtown area. The Sheraton Symphony Hall sits up on the hill above the Gaslamp and is also a bit of a hike. The Westin San Diego Downtown is about a block and a half away from the train station. A good thing about them is they offer airport shuttle.
Since I've stayed at 4 out of 5 of the downtown properties as well as the Sheraton Marina I feel like I can be of help here. If I were choosing, I'd likely choose the Westin Gaslamp. But of the 2 you mentioned I'd probably begrudgingly choose the Grant because it's more centrally located. If you'd asked me that a year ago it would have been the Grant hands down. But the vibe I got from my last stay did not leave me feeling good about returning.