The People's History Museum is close to the Lowry Hotel and is free and a bit different so I'd start there. It's also quite small so won't take very long.
I'd go up Bridge Street to Deansgate / St Ann's Square for the proper Victorian Manchester buildings and then onto the City Art Gallery.. They have a room with paintings of Manchester and Salford by Lowry and Adolphe Valette.
Unfortunately the Town Hall is covered up but the central library is a beautiful building, as is the Midland Hotel. Afternoon Tea at the Midland is lovely.
Other people might be better help with food. We tend to go to a little cafe near the library called Hampton and Vouis that has good vegan options or to Spinningfields off Deansgate. It has much more modern buildings and fairly generic restaurants but you can take the lift at 20 Stories for great views of Manchester. You can get coffee or cocktails there if you want, but you don't have to. You can just have a quick look. Alternatively at the bottom end of Deansgate is the Hilton Hotel which has a high level cocktail bar with great views of the new tower blocks that have recently been built that are nicknamed Manchattan.
Spinningfields is also not far from your hotel, being mindful that you only have 4 hours.
Depending on how much time you have, Castlefield Viaduct is near Spinningfields and is Manchester's new but small answer to NYC's High Line.
Alternatives would be the Science and Industry Museum at the bottom of Deansgate or you could head to the University district and have a look in the Whitworth Art Gallery and the newly done up Manchester Museum. The Whitworth has a lovely glass cafe surrounded by trees.
I'd avoid Piccadilly. It is grotty at the best of times and is currently a building site!