There are two or three things to consider in making your decision as to how to get to Vilamoura from Lisbon.
1) Vilamoura is not the Algarve! It a modern Golf/Marina Complex. There are regular public buses to Quarteira and Albufeira during the day but if you want to explore the Algarve during your week here, a hire car is highly recommended.
The region is only about 160km by 40 km but its wide diversity from the wild rocky west coast, the historic town of Lagos where I live, to the inland hills and the Spanish border, is very difficult to explore without a car.
Consequently, you might consider hiring a car.
If you did, I would recommend picking it up at Lisbon Airport on your departure from Lisbon, cross the Tejo by the Vasco da Gama bridge and take the toll-motorway to the Algarve. On arriving at the A22, bear left on the the Via Infante Motorway and continue until you come to the Loulé/Almancil/Quarteira/ off ramp, bear right until you come to Quarteira and follow the signs for Vilamoura. (Transit Time with stops - 3 hours.)
A reputable hire company in Lisbon is Auto-Jardim.
You can see details here:
http://www.carhireyes.com/autojardim/
If you follow this option make sure you specifiy if you need an automatic, as most vehicles this side of the pond are manual shift.
2) If you really just want to relax in the Hilton, or not hire a car, I would recommend the train as it is a wonderful trip over the 25 Abril bridge and through the Alentejo. There is a cafe on-board and it is a wonderful relaxing way to spend 3,5 to 4 hours.
There are two types of Intercity - Alpha Pendular & Intercidades.
- The first operate twice daily from Lisbon Gare Oriente, via Lisbon Entrecampos stations to the Algarve. If you are staying in a central Lisbon Hotel the second station is the one you want.
- The second type are called Intercidades and follow the same route but stop at more stations and operate three times a day. There is a fourth evening service on Fridays.
You can find the timetable on my blog by scrolling down on the right hand panel, until you come to the section entitled:
>>>> Algarve & Portugal - Travel Transport Links
Click on the item
>>>> # Portuguese Railways - 2008 - Lisbon - Algarve Faro/Lagos Timetable
You will be able to download it in pdf format.
For Vilamoura you will want to detrain at Loulé Station. There are often no taxis there but am sure you can ask the Hilton to have one meet you. It will take about 15 minutes from there to Vilamoura. Alterntively, continue to Faro Station where there are always taxis. It will take 25 minutes to Vilamoura and cost about € 25 to € 35 depending on time of day/week.
3) If buses really are you preference, bus operator RENEX operate several services daily from Lisbon Gare Oriente (same as the train station) to Vilamoura.
You can find the timetable on my blog by scrolling down on the right hand panel, until you come to the section entitled:
>>>> Algarve & Portugal - Travel Transport Links
Click on the item:
>>>> RENEX Bus Service - Lisbon to Algarve timetable
Look at the the top panel entitled Lisboa - Loulé - Lisboa
N.B. "P" means departure / "C" means arrival.
Note that there is no Metro link yet to Lisbon Airport. On arrival you will need to grab a taxi or bus to your hotel.
Operator Rede Expressos also operates this route. Buses leave from Lisbon Sete Rios Coach Station (Metro Jardim Zoologico.)
I have published a copy of the relevant timetable here:
http://www.scribd.com/doc/2929565/3seteriosvilamoura
Hope this helps and thanks again for contacting me.