Sorry to you got caught in that hurricane. Hopefully your spring season can be a successful one. So I hunt the Northern part of New Mexico and have luck getting on birds there year after year. The most popular areas in the state are in the Gila and Lincoln National forests, so you would be dealing with more birds but also more people down there. I would say start by picking a national forest to start. The Carson, Santa Fe, Lincoln, Gila, and Cibola are the main national forests in New Mexico for turkey hunting. There are birds down lower on patches of BLM and state lease land, but there is a lot more map work and research to be done in order to hunt these areas. They are also more primarily areas for Rio Grandes.
Once you get a forest in mind that you want to go for I would say narrow down your search to a specific side or piece of that unit and find areas with water even seasonal tanks and springs to figure where you want to go to hunt. I will find gobblers in areas that don't have any water in the canyon at all as they do travel a lot off the roost, but the odds are they will have to come through the water areas at some point or another in the course of a day. I would also pay attention to the weather as it gets closer to your hunt or deciding where to go. The amount of snowpack we get has a huge impact on the movement of birds and where they will be. This past winter was rather dry and many hunters I've talked to have said the birds were not where they usually were at that time of year, although I will say that I was able to get into gobbling birds throughout the season.
Most of the residents will hunt the first weekend of the season, and pressure tapers off after that. It looks like this next year is starting on a Monday which can be good. I've gotten into gobbling birds throughout the season like I've said, but I would go with the start or end of the season if I was hunting from out of state.