What to do with an 8 hour lay over in Lisbon

I would take the metro or a taxi from the airport, pick one--maybe two if they are short--things/places you want to do or see. I would get back to the airport with at least 2.5 hours to spare (some people will take greater risk than that, but I wouldn't). Rick's Baixa Stroll is nice. You don't have time IMO to get to Sintra and back, at least not enough time to enjoy it.

Lisbon airport is inside the city, closer to the centre than most other European airports. It therefore will not break the bank, and will not take long, to get a taxi to the city centre, and back again. Do not hire a driver as the centre is pedestrians only.
Lisbon city centre fronts on the river and surrounded by hills on 2 sides. There is a large square on the waterfront (Praça do Comércio). It is very walkable. If you want to follow a pre-set walking tour, its up to you. I would just explore, and stop in a café when tired. It is difficult to get lost, the streets are in a grid.

So sounds like it's easy and quick to get from the airport to Lisbon but nothing to see? Just eat and walk?

Janet, what to see is the whole city. For example, click here for a photo of Praça do Comércio, or here for one of the streets in the city centre. The whole city centre is worth seeing.

There's a ton to see and do! You could go up to the castle on the top of the hill (either take the #28 trolley there or a taxi or tuktuk) for amazing views and explore the castle grounds (wild peacocks wandering around are fun), as well as stroll through the neighborhood around the castle (the Alfama) for narrow cobblestone streets, alleyways, and the most beautiful tiled buildings.
Another neighborhood to explore is Chiado/Bairro Alto (upper neighborhood), which is also up a hill. You can get there by walking or take the Santa Justa Elevador from the center of town up the hill (it's strange but it really is just a big elevator that takes you from the bottom of a hill up to the top). Again, amazing views and there are some museums up there I believe (one is in the ruins of the old Carmelite church at the top of the hill). There are also various art museums, a tile museum, and a fado museum (Portugal's traditional music) if any of these interest you.
Also, the neighborhood of Belem is really cool. It's about a 20 minute ride outside the center (#15 trolley or tram or you can also take a taxi)...its got an amazing monastery and several monuments celebrating Portugal's empire during the age of discoveries. Also in Belem, a famous bakery with delicious Portugese custard tarts.
If I had to choose, i would take a cab into the center (praca do comercio), wander around that area and up Rua Augusta (the main tourist pedestrian area...lots of outdoor cafes and street performers) for a half hour or so to get a feel for it, and then go out to Belem, spend maybe two hours there (you can easily see everything in that time) and then head back to the airport? Good luck!

Thanks Ilana. Huge help!