Lisbon

Been to Lisbon a few times...

Go to Pasteis de Belem:

http://www.pasteisdebelem.pt/en.html

next door is Jeronimos Monastary:

http://www.mosteirojeronimos.pt/english/index.html
and across the street along the waterfront of the Tagus River is the Tower of Belem (same website as above) and the Discoveries Monument.

Also nearby is the Coaches Museum:
http://en.museudoscoches.pt/

From this area, and a 30 minute walk (5 minute taxi ride) along the Tagus River (going east)is group of restaurants/docks called "Docas" http://www.golisbon.com/sight-seeing/docas.html A very beautiful area beneath the bridge "Ponte 25 de Abril"!

Leave enough time for traffic and check-in to get back for your flight!!!!!

Lisbon is beautiful no matter what you decide.

Carl's advice is very good, Belen is a highlight of Lisbon. Also there is the monument to the explorers and the watch tower overlooking the mouth of the river. And the pastries he recommends are unbelievable!

It can be a 20-30 tram or taxi ride from the city center and traffic can be heavy, so factor that in.

If just in the city center, stroll the main pedestrian avenue, hike up to the castle or explore the opposite hillside with the ruined church. Maybe try some ports at the sample store at the top of the hill above the incline. You could see a lot in about 3-4 hours of walking.

Any first visit to Lisbon should include a trolley ride up to the castle overlooking town, and then a stroll back down through the Alfama neighborhood. Agree on the side trip to Belem.

Lisbon is great, and deserves more than 6 hours, though. You can't squeeze out another day or two?