October isn't exactly beach weather in Portugal - even in the Algarve. The average high temp is around 66°. Much of the Algarve will be shut down at this time. When I was in Portugal 2 years ago, I picked up a car at the airport and than drove to Evora. From there, I went to the disused town of Castelo Rodrigo with a population of about 50. I stayed at a B&B called Casa da Cisterna which was wonderful. The owner arranges trips to visit the prehistoric petroglyphs in the Coa National Park. She has a key to the gate and takes you at dusk which is the best time for a visit. From there, you can head to Porto through the Douro Valley wine area. Some great Quintas for tasting and some nice places to stay. From Porto, you could head south stopping at Coimbra, Batahala, Alcobaca, and stay the night in Obidos. Then a night in Sintra before ditching the car and spending at least 3 nights in Lisbon.
In Evora, I stayed at the Pensao Policarpo - very small town Portugese hotel, quaint, convenient with a great staff, free parking and a good breakfast. David, the owner is a an excellent host. One of the best restaurants I visited in Europe is Botequim da Mouraria in Evora - only about 15 seats, you sit at a counter and get a gastronomic delight - get there early or you'll wait. In Castelo, you might want to try the home cooked meal at Cisterna - reasonably priced and typical of the area. In Porto, I stayed at Hotel B&B Porto Central. It's a modern hotel, not a B&B, with onsite parking and is centrally located for sightseeing. The well regarded restaurant Abadia is a short walk away. Great seafood, old-world service, try the grilled octopus! In Lisbon, I stayed at Brown's Downtown Hotel on Rua de Vittoria. Great rooms with a kitchenette, tastefully furnished, chic. Centrally located to take Rick's three walking ours, near the river, close to a Metro stop.