I am going to the Algarve for just over 4 weeks from mid March to mid April, so I don't think 2 weeks is too long! Having said that, I have been lots of times and this for me is just chill time, to avoid the miserable British weather and hopefully get some beach time, rather than exploring.
The Algarve is mainly about the beaches and golf - if these aren't your primary concern, then look at the Alentejo instead.
The middle two weeks of April are Easter school holidays and therefore very busy (and more expensive). I booked my accommodation last April.
Evora is certainly worth a couple of days as is the coast around Setubal and Comporta. The coast between here and Aljezur is worth exploring too.
If you are set on the Algarve, I would suggest a week in Lagos and a week in Tavira.