This day trip takes you to the east, for a Sotavento circuit of the leeward (sheltered) parts of coastal Algarve, almost as far as Spain. It's not that long a trip - 94 km (58 miles) - but with plenty to see and do that will enhance the enjoyment of your Algarve holiday.
Olhão
An easy 10 km (6 miles) drive from Faro, this fishing port town has intriguing Moorish architecture, with narrow, winding streets and distinctive flat-roofed houses.

Olhão's modern market buildings
The port-side road houses two large new market buildings which sell fish and food respectively. But, the nearby grassed areas have tiled memorials that bear witness to the the more distant maritime past.
If you're anything of an artist and want to explore the Algarve in search of subjects, you might like to try your hand at capturing the splendid Igreja Matriz church. It has a wonderfully ornate frontage (or maybe you could try a sketch of one of the life-size statues of the angels on either side of the altar).
Fuzeta
Another 10 km (6 miles) to the east, Fuzeta is a small detour off the N125 coastal road between Olhão and Tavira. The place is an example of how Algarve's traditional way of life can be preserved, thanks to the efforts of proud local inhabitants.

You could enjoy a trip on the water taxi...

Or visit the Marim Estate, within the Ria Formosa Nature Reserve, where you will enjoy evocative glimpses into the region's history (such as old tidal mills).
Birdwatching enthusiasts happily spend whole days in the reserve, which is home to a wide variety of avian life (and, perhaps, lost tourists!)
Tavira
Tavira has much to recommend it, and is one of my very favourite Algarve places.
Park if you can in the main square (Praça da Republica). There is much to explore, including churches and monuments commemorating its importance to the area in previous centuries. (Or you can take a pedalo trip along the river - a different way to see the sights, and highly recommended).
The riverside cafés and gardens are high on my list of places to be during an Algarve holiday. And I don't suppose I'll ever tire of the magnificent castle or the Igreja, whose clocktower is shown here.
Cacela Velha
This is an original Algarvean fortress town, predating even the Moorish period. In its present form, the massive walls were reinforced to resist the onslaughts of Napoleon's troops during the Peninsular War in the early 19th Century.
It has landscapes to wow you and tons of stunning views. Do not forget your camera!

Vila Real de Santo António
Next to the Guadiana rivermouth, Vila Real has an unusual central square with cobbles laid in a radial pattern, within a geometric grid of streets that were re-built in the 18th century by the Marques de Pombal, a rich aristocrat.
While you're there, tour the old market for a feel of the local culture, and, if time allows, visit the church.
Admire the panoramic views of Spain just across the river.
(You could even take the ferry and visit Ayamonte - lots do).