There are no direct public transport links between the Algarve and Valencia. Further more there are no low cost airlinks between Lisbon and Valencia.
The distance is about 929kms.
The only realistic options are:
1) Air from Faro Airport.
Air Berlin have a regional hub in Palma de Mallorca. Their summer timetables may yet change. At present they are showing a flight Faro - Mallorca - Valencia (change in Palma) for a very reasonable price.
The only problem is that at present it only shows as operates as a through connection on Wednesdays.
site: http://www.airberlin.com
1) Bus/Air -
Renex Bus from Alvor to Lisbon Gare Oriente. Taxi/Airport Bus to Lisbon Airport
Then low cost airline Vueling/Easyjet to Madrid and then low cost airline Clickair/Spanair/Ryanir to Valencia.
2) Bus/Bus
Take the Daily EVA/DAMAS bus from Portimão to Seville and then connect with an alsa.es bus from Seville to Valencia.
Check Cubsur's site here for information on the Portimão to Seville Services:
http://thomasallen.home.sapo.pt/travel/001.htm
Alsa schedule is below:
Current Daily Departure schedules : SEVILLA - VALENCIA
Seville Valencia
depart arrive € €
10:00 21:25 49,86 94,73
10:00 21:25 49,86 94,73
16:30 02:15 next day 56,79 107,90
16:30 02:15 next day 56,79 107,90
22:00 09:15 next day 53,20 101,08
See: www.alsa.es
It may also be possible to get a low cost flight from Seville to Valencia but I do not recommend it as getting to Seville Airport from the Algarve is a pain unless you have a car.
Train is not an option as there are no suitable cross Iberian Peninsula services.
