Hi!
Sorry for the delay in reply.
Faro Bus Station is right downtown. Most of the small hostels and pensions are within 5 blocks of there. Taxis may be available at the rail station 200m but probably will not want to carry you such a short distance.
The problem is that downtown Faro at 01:45 a.m. is not the best time to be downtown Faro as the bars are closing and it is a bit unsavory unless you have someone to meet you.
I would suggest that you try to come in on the 07:30 or 16:30 from Seville Plaza das Armas.
Be aware that Faro is the District Capital and a business center. It is not exactly a tourist center and you could probably do the old centre in a couple of hours.
I would suggest that you consider laying over in Tavira or going straight to Lagos.
If you do decide to lay over in Faro and come on the 01:45 train, I would recommend the following pension which while perhaps a bit over budget is clean and near the station and bus station.
http://www.residencialalgarve.com/
As regards driving, bear in mind that if you want to pick up in Spain and drop-off in Portugal it will cost a lot.
Additionally, if you are travelling between 1st June and 30th September you should remember that the interior of Andalucia and Portugal is very very hot. You shoulld plan to travel early morning and finish by 12:00.
If you are from "over the pond", bear in mind that most car rental vehicles here in Spain and Portugal are manual shift. Automatics attract a premium.
Transiting Seville can be a bit of a head-ache during morning rush hour, lunchtime and afternoon rush-hour.
Also from 15th July till 30th August, all roads are going to be chaotic owing to the lemming-like mass European migration from the North of Europe to the shores of the Med and Atlantic.
Road signage in Portugal and Spain is usually pretty good particularly on main routes.
A final possible option would be to take a budget evening Spanair flight from Granada to Madrid and then the next day the daily Ryanair flight from Madrid to Faro.
From Faro you can get a transfer, taxi or hire car to Lagos.
For more info see previous postings I have made on my blog at http://barlaventostravelblog.blogspot.com.
Also check out:
http://www.solpraiaferias.com/index.php?content=cheg_en
hope this helps.