About how many days do you think would be appropriate to allot for Lisbon if I'm only going to see the main city sights?
2
Ed's right. But a shame not to visit Sintra while in Lisbon.
I would give it three. The Gulbenkian plus the old art museum, a full day for Belem. And another day to explore the Alfama, the upper neighborhood and the lower one. That does not even count Sintra which is a must -- even better to stay overnight for two nights there.
I would do 3. Sintra was amazing and takes a full day. Belem is good for about half a day. The rest of the time in central Lisbon. I would recommend taking one of the walking tours in Lisbon.