Are you a week in the Lisbon area and a week in the Algarve?
Don’t forget Kidd’s Comporta Dunes which should be open by July and looks excellent.
That aside, West Cliffs is really good up north (better than Praia d’el Rey and certainly Obidos) and the small Pine Cliffs nine holer is a mini-Cypress Point down south (do NOT go in with that high of an expectation!). Monte-Rei typical Nicklaus but in a good setting without any houses built yet. San Lorenzo beautiful holes down by the lagoon but tired and very 80’s design.
I love Portugal. IMO it has the best 'ordinary' food of anywhere I have ever been, there are beautiful grilled sardines and suchlike virtually everywhere.
Golfwise, I echo what Ally has said. Praia d'El Rey is nice, but has been significantly impacted by housing, whereas West Cliffs is newer and doesn't have the same issue, or it didn't four or five years ago. I saw Comporta during its original build ten or eleven years ago (the developer went spectacularly bust, and it lay fallow for most of the intervening years). I thought then that it would be the best course in Portugal as soon as it opened -- I'm going to see it next month to check if I was right.
Monte Rei I saw perhaps fifteen years ago. I think Ally is a little harsh to call it a 'typical Nicklaus', but it is big and brawny. When it opened, I remember thinking to myself 'This is the best this course will ever be' because the plan was for all the high ground between the holes to be used for housing, but they don't seem to have built many/any.
I haven't seen Troia but would like to. Ditto the Pine Cliffs nine holer.
Discovery Land has built its first European project at Costa Terra, not far from Comporta, with (inevitably for Discovery) a Fazio golf course. I assume it will be extremely difficult to get on, but am not sure. I only know one person who has seen it, and he wasn't a fan, but mileages will undoubtedly vary.
Of the older courses in the Algarve, I'm not a fan of Penina, it felt very very tired when I was last there. I liked the original version of Palmares, and liked the RTJ2 rebuild quite a lot too. In general I feel that the standard of Algarve golf is significantly higher than of that on the Costa del Sol in Spain, a couple of hours east.
Lisbon is a magnificent city, one of my favourite in Europe. I recommend taking the historic no. 28 tram, which goes through a lot of the oldest and most interesting parts of the city and will give you a good tour. I also recommend a wander through the old Alfama district, popping into bars and restaurants as you choose. And a trip down to the waterside at Belem is worthwhile too -- the maritime museum is good and there is the cafe that invented the pastel de nata, for which we should all be grateful -- a good espresso and one of them is the perfect midmorning snack.