Hi Phil,
I think you'll love Lisbon, and you should be able to see quite a bit even in just a day or two.
Castelo de Sao Jorge is a great option for a singular sight. It's also close-ish to the Tile Museum if that's a must see for you. The castle is definitely more of a place to walk around and explore than a museum (although there is a small museum with archeological finds on the grounds). Great views of the city from every angle too.
If your goal is to be in Belem, it would be more convenient to see the Jerónimos Monastery, which was also a highlight of our trip. The building itself is gorgeous and has a ton of Portuguese history packed inside. It's also right next to Pastéis de Belém which is a great spot to try Pastéis de nata.
Also if you make it out to Sintra, I can't recommend the Castelo dos Mouros enough. Once again, not much in the way of exhibits there, but standing on a windswept castle wall looking off into the Atlantic is a pretty cool moment. Pena palace is also a neat stop, but in my opinion the outside is better than the inside since you'll be crammed in with a thousand other people unless you're there for the first entry slot.
If you do end up having extra time, we still talk about our stop at Bifanas do Afonso on a weekly basis. Great (and fast) local sandwich. You can grab a bifana and a Sagres beer, sit down on the curb and possibly have the best meal of your trip.
