I suggest for short rentals like 1 or 2 days, you choose between British Airways (with which you'll earn a flat 500 miles, with a bit of a bonus if you rent crediting to BA something like 4 times a year, but may not work if you use some corporate AWDs; BA suggests their own AWDs like N744100 for BA Blue, though I don't know if they're really necessary) or Southwest (which earns a flat 0.5, unless there's a bonus going on in which case it may earn more though usually on 3 day or longer rentals, not 1 or 2 days). Other airlines will only earn you 50 miles a day, thus 100 miles for a 2-day rental.

You can choose a different partner (or not partner) for each rental, btw. I have British as my default (using it only for short rentals, it's a simple way to keep my BA miles alive), but regularly change it to AA or UA or DL on longer rentals, typically based on who's got the best promo (there's a whole thread here in the Avis forum dedicated to listing the various Avis bonus miles promos). The partner doesn't go in your profile. However, a default AWD does (and thus note any possible interaction of that with choosing BA as a partner). In my case N744100 is my default AWD, and I have changed it when using other airlines, but leave it be when using BA.

You can evaluate hotels yourself. Each has different earning rates, and some like Hyatt are per rental while others are per day. It's possible that one of them may make more sense for 1-day rentals, while another may make more sense for 2-day rentals.

Here is the part of the Avis website where you can look up the earning rules for all their partners, one by one:

http://www.avis.com/car-rental/content/miles-points.ac

Note that a couple airline and hotel partners seem to be misfiled under the Other Partnerships dropdown (rather than being in Airlines or Hotels).

One other thing of note that bothers some people and not others: For domestic airlines, Avis (as well as other rental companies) charge 50c for up to the first 4 days, while AFAIK that doesn't happen with foreign airlines (like BA) or hotels. I don't mind paying $2 when I'm earning thousands of miles on a bonus promotion for a 4-day rental, but I wouldn't like it as much if I was only earning 50 or 100 miles...