Most of my favorite shops are a little further away from downtown and unfortunately won’t be the easiest to get to. There are a few good shops in the downtown area though...
Downtown: Blend by Davidoff
North Side: (very close to downtown): Burn by Rocky Patel
Those will be the closest to you. Both are great but are the highest priced shops in the area.
Strip District: Leaf and Bean (also very close to downtown, great shop.
South Side: Bloom, also close but further than the other ones. This place is like walking back in time 50 years. I like it but it’s an acquired taste.
South Side: Drawing Room, this place is newer. It’s technically a private lounge but since it’s still new they often have public events but access will be hit or miss because of that.
Close to the airport, away from downtown: Smoke Stack in Moon Township.
Your best option like others have said is to order online mostly because of your options near downtown.
if you do have access to transportation, some good options for Padrons would be Cigars International in Bridgeville (about 20 minutes south of downtown), Old Allegheny (also about 20 minutes from downtown), Smoker Friendly (several locations around the region it’s actually a smoke shop not just cigars but they do carry Padron.