No recomendations, but if you are going to stay 3 weeks you should get a nice hotel at $40 a day.
Whatever the daily rate is, aim to half it for a 3 week stay, with a cash payment, not credit card as there are hefty commisons for the hotels to pay on credit cards.
It will be unlikely that you have all the pesos on you, but tell them that you will be changing money shortly and you don't want to pay all the money up front, just in case the room is nice, but there is a lot of noise etc.
I stayed in Cali nearly 3 years ago for 2.5 weeks and got a nice 1 bedroom Suite in a nice hotel for 60,000 pesos a day, plus breakfast, the daily rate then was 125,000 pesos.
You won't be able to do this via the web, but when you are stood there in front of them it should be easy as long as the hotels are not full, due to some event going on, which they aren't most of the year in Cali.