Women should probably not travel alone in Gallup. While most locals seem to stick to themselves and mind their own business, you do get quite a few who seem to be a little too friendly, to the point where one feels unsafe - and that was during the daytime. At night, lone women travelers would be best to stay in your room as there are hardly any women downtown Gallup after dusk.
There are always a few 'drifters' hanging around the bus/train station and its dimly lit appearance adds to the eerie ambience. If you are a lone woman traveler through Gallup, tuck away valuables and look like you don't have any money. They probably wouldn't rob you, but they will strike up a conversation and at the end, ask you for a couple of dollars.
If traveling by bus or train, be sure to call the station ahead of time to make sure your transportation in on time, as the train is frequently running late and the station has inconvient hours. There are few people around in the mornings and there is always safety in numbers.
The only warning I can think of is not to drive on Hwy 264 towards Window Rock or on Hwy 491 (formerly Hwy 666) at night unless you really have to. There are two reasons for this that are both equally important.
1.) Drunk drivers and bad medians: there is absolutely no medians in between you and oncoming traffic on many areas of these highway. Many people die on these roads as a result of drunk driving accidents. The reservation is dry which causes people to have to drive long distances to access alcohol and to get home.
2.) Animals in the roadway. At night it is nearly impossible to see horses and cows in the road. Every time I've driven on 264 I've seen a dead horse or cow or both. Not only is your car wrecked if you hit one but you are also responsible for paying the owner for a new animal. This can be $2,000-$3,000 dollars. Bottom line: Don't hit one.