It is not officially possible to connect two external DVI monitors to a MacBook Air.

Ideally this can be done through the thunderbolt connector with an adapter to drive both displays, but otherwise can anyone recommend a decent USB3

DVI adapter is acceptable if it's equal to or better

I'm not watching movies or gaming on the displays, as this is just for work which consists primarily of programming so maybe a USB -> DVI adapter would be acceptable as well.

Apple's support article states that you can only connect one non-Thunderbolt monitor per Thunderbolt port.

Additionally, you can look at hooking a second screen up via USB, using a product like those made by DisplayLink.

The MacBook Pro described in that post has similar options/limitations as your MacBook Air when it comes to multi-monitor setups.

There recently was a similar discussion here at Ask Different: Two Monitors Setup On a MacBook Pro

Connecting through Thunderbolt is possible

It's not a simple adapter, it's active, and it's quite expensive.

You can however go with a MiniDP - DVI adapter for one monitor, and let USB 3 handle the other one.

TUAW featured one from Kensington recently