1/ North-East of Quito : Cayambe (5790m / PD)
East of La Paz there is Antisana (5758m / PD), but less accessible than Cayambe
2/ South-East of La Paz :
Illimani (6438m / PD-AD) + Mururata (5864m / F) ... close to each other
You can also easily go to the border between Chile and Bolivia (5 hours from La Paz by bus / car) to climb Parinacota (6342m / F) + Pomerape (6282m / F) right beside to each other, and a bit further away Sajama (6542m / PD) the highest mountain in Bolivia.
3/ As far as weather is concerned, it's good for both. By the Chilean border it may be more stable as this area is quite dry in general.
4/ And if you find it hard to make up your choice, get a copy of John Biggar's book about Andes summits. The best database about Andes on a book !
http://www.andes.org.uk/andes-guidebooks.htm