4 Days in the Algarve: Where to Go?

I have a trip booked for almost 3 weeks, starting end of May and ending in Faro, Portugal early/mid June. Travelling with my friend, 21F, and we are wondering where to go in the Algarve region of Portugal. We leave from Lisbon, and we're thinking of taking the train down to to the Algarve, spending 5 nights there (arriving in the evening the first night), and then leaving out of Faro to head home. We want to end our trip with some fun, so good night life and spending the days at the beaches there. I am wondering which areas are walkable to both of these options, and hopefully a bit less touristy. Should we stay in one spot for the 5 nights or do 2-3 nights in two different areas along the way from Lisbon to Faro? Looking for any low-cost recs to make the most of our time there!