I'd say head north - rent a car and do Lisbon to Porto, making stops in Nazaré, Batalha, Óbidos, Coimbra, Aveiro etc. That can be done over one or two days. If you want to do it by public transport - trains are always an option.
Sintra is a nice day trip from Lisbon.
Porto is no longer gritty thanks to tourist euros. Some of the hotels you're considering are far from everything.

Sheraton Lisbon is in a decent location, Altis Belém is also in a great location right on the river. It's also smaller than the Sheraton.