Our family (2 adults, 1 4-year old child) spent a lovely week in Portugal in late March and early April. A few random thoughts:
The weather was dreamy. Low to mid 70s all week and lots of sunshine. That certainly helped the cause.
We landed in Lisbon on Saturday morning and drove immediately to Lagos, staying in the old town there for 4 nights before returning to Lisbon for the last few days (flying back home on Saturday).
A 2-hour wait in passport control on the way in, but probably a 15 minute combined check-in, security and passport control on the way out. Lisbon Airport is somewhere I'd recommend planning for a little extra time just coming and going.
Lagos was perfect for us. We stayed in an AirBnb in the old center, walking distance to the beach and harbor front, along with lots of restaurants and shops. The town is particularly charming in the evenings when the old town remains buzzy but not overcrowded, at least in late March.
We drove all over the Algarve, visiting Tavira and Altura in the far west (nearly to the Spanish border), back to the amazing sand dunes at Praia da Bordeira on the Algarve's Atlantic coast. The beaches were clean with perfect sand - too cold for swimming now even with warmer temps, but I'm sure they're quite a scene in summer. I think exploring the Algarve would be very difficult if you didn't have a car - while there are buses and even some trains, it seems public transport is limited.
A boat tour off the Algarve coast outside of Lagos was a highlight. The sea caves and sandstone formations are so amazing, though apparently ravaged by particularly heavy winter rains this year according to locals.
We loved our visit to Tavira, but were glad we were staying in Lagos. It seemed to us that Lagos was a better spot for a home base if you're looking to explore the area, though Tavira has lovely riverside parks and a beautiful castle worth exploring.
Lisbon has a lovely chaos to it, from its traffic, its tangled and heavily cobbled streets, to its heart-stopping hills. Some parts are wildly overrun with cruise people and group tours (e.g., areas around the Lisbon Cathedral and Praça do Comércio, but it's not hard to get away from the tourism groups by turning off the main drag for 5 minutes. We did not do enough to maximize our time there, but we absolutely loved the Barrio Alto neighborhood, especially after dark. It had more charm than some of the other parts we visited. We took a sunset cruise on a sailboat which was lovely (but very cold out on the water as the sun went down!) and found some wonderful places to watch the sunset in town as well (e.g., Edward VII Park). Public transport options are plentiful and come with an easy-to-use transportation pass, but Uber is a great and very cheap alternative when you need to get somewhere quickly.
We did a day trip with a private guide we booked through our hotel to Cascais and Sintra. Cascais was a mellow and very wealthy town that we could have wandered around for another day or so if we'd have the time. Sintra, unfortunately, was wildly overrun with tourists (including us of course) on a Friday afternoon and that definitely hampered our enjoyment. We didn't plan it well, so the visit to the town itself and Pena Castle I'm sure would have been more enjoyable had we planned for a less busy day or time.
The food was excellent all week, and everything is pretty affordable by comparison to many other places in Europe. A beer and a snack will still run you 5 euros or so in Lagos (slightly more in Lisbon). You can eat really well in Portugal and there's always salads and fresh produce to choose from, as well as fresh seafood. The TimeOut Market in Lisbon is a great sport for lunch but was very busy at lunch hour as you might expect (hard to find seating).
Overall a great trip to a country we'll want to go back to again!