Looking for a cheap wide angle for a6000

Over the summer I will be taking a trip to the southwest with stops in New Mexico, Utah and Colorado and I would like to have a good wide angle lens to capture landscapes. I am not opposed to manual focus or using adapters or with other lens mounts. Currently the widest lens I own it a Nikon AI 28mm which on the cropped sensor is equivalent to 42.5mm which is much to narrow. So far I have looked at the Sigma 19mm and the Sony 16mm. I can spend a maximum of $200, but would like to keep it to under $150.