Honest answer is it depends on what type of experience you're looking to have. I've stayed at a number of different downtown hotels but pretty much all of them are ridiculously priced for game day weekends. We've been using AirBNB lately and finding better value. The cheapest I've ever stayed was by staying in Greentree which is a suburb just over Mount Washington and is a very short drive if I remember correctly through the Fort Pitt tunnel. You are definitely outside of the city which makes anything else you might want to do or check out in Pittsburgh kind of a pain in the *** since you have to drive or take some other mode of transportation in. Greentree has your typical Holiday Inn, Hampton Inn type of hotels but for a guys weekend of drinking and catching the Steeler game it was fine. (Roughly $100 a night)
Downtown is much more convenient, walkable, and provides a lot more entertainment right outside your door. Advantage to staying at most of the downtown hotels is you can park your car and leave it for the weekend but you'll have to pay for that too. I'm not sure if it's technically downtown but Station Square has been mentioned and is a good option. It's a couple block area on the south side which means the south side of the Monongahela River or opposite the stadium. It has a few restaurants like the Hard Rock, Melting Pot, Grand Concourse, a few bars and shops and access to both inclines. Great game day experience is taking the boat across the river to Heinz. I'm from Michigan but I kind of view this area as more of a tourist spot but I could be wrong. (Stayed at the Sheraton a few times probably between $300-400 a night) My go to hotel used to be the Hilton (I think it has changed to the Wyndham Grand) it sits right at the point so between the Monongahela and Allegheny rivers. Liked this spot because I could park and not need my car all weekend, can walk to a lot of different places. The stadium is right across the bridge so if you are meeting or going to a tailgate it's a few minute walk, if your taking your vehicle a 2 minute drive. On game days they close the Roberto Clemente bridge which is about a 5 minute walk and has a few bars with game day crowds. The hotel is also close to Point State Park, PNC, tons of bars, shops etc. Strip District not too far. Really in the middle of everything. Not sure if it's still a thing but in the early to mid 2000's it wasn't out of the ordinary to run into current and former players there. Used to be some autograph hounds in there and although I didn't approach them I saw Ryan Clark, Marvel Smith, Max Starks, Alan Faneca and Kevin Greene all there. (Also 300-400 on game weekends)
Over the last say 8/10 years AirBNB has been my go to, lots of different price points and depending on group size I find this to be the best value. If it's just my wife and I we found a small studio apartment on the North Side within walking distance of Heinz for $130 a night in an area they call Germantown, parts of the neighborhood are a little sketchy but others are very nice, unfortunately the owners have gotten hip to the game and have increased it to 230 and put a 3 night minimum on it. If we are going with a larger group we use a large home up on MT. Washington that overlooks the city and is just above Station Square. This one is pricey at $850 a night but sleeps 8 so when shared it's much more affordable.
Hope this is of some help. Please keep in mind these experiences stretch back a number of years so I'm sure prices, names and places have changed but this should give you a general idea. Pittsburgh is a beautiful and fantastic city but is tough to get around for us out of towners, looking at it on a map looks like everything is super concentrated but remember there are 3 rivers, mountains and tunnels to navigate. What looks like an easy walk may not be. One last thing I would recommend taking the stadium tour which are available on non- game days. I think they're like ten bucks but well worth it. These were available pre- Covid so make sure they still do them you won't be sorry. If you have specific questions feel free to PM me if I could help I would be glad too! Apologize for the long post.