Also, Im riding an eFat Bike, (no throttle) are there resrictions on any of the trails?
Here's a good map of Tijeras area: https://www.dogofthedesert.net/manzanitas-trail-map/
As bronxbomber25 mentioned, most of the Tijeras trails are fine for motorcycles so you should be ok on east side of the road, but not 100% sure about Tunnel and Otero). However, you didn't mention your skill level, nor fitness level. How many miles and how much climbing can you do? eBike doesn't grant superpowers lol. And you said "safe" so makes me wonder. There's some steep stuff out there, lots of rock gardens, so even if eFat it might be too much. Faulty and Bird House I would pass on. If you are beginner/intermediate, parking at Oak Flats and doing Mohogany out and back is one option, as is the Ponderosa loop, neither one is particularly technical. Gamble Oak is a fun one to me, has good flow, but gets rock gardeny in spots. Parking at Pine Flats and going up Deadman to the steep section and back is good if you don't want a long ride. If you are in shape and can handle technical, go all the way up on Deadman (take right side just off the dirt road, might be called Deadman Alternate), then up on Oak Flat Connector then head south on Easy Pickin' over to Mohogany and then back down Gamble Oak. You might have to hike-a-bike a few spots. One of my favorite trails is Pine Flats-Deadman-Southern Crossing out and back, mix of technical rock gardens and flow, but I'm a solid intermediate rider who is used to rock gardens.
If you are in Albuquerque proper, you'd have to research the rules for Albuquerque Open Space but the trails in the Sandia Foothills from the Spain trailhead and from Indian School trailhead are all good ones. I don't ever see rangers so as long as you're not a jerk on the trail or running people off it you should be fine. If you are in Rio Rancho there is a fat biking trail system, can't remember the name. Placitas on the north end of town is probably a good eFat trail system, park at the 2nd parking exit up the hill and head off to the east then circle back to the south, then take Bobsled, it has some small jumplines if you like that. They're small enough you don't have to jump them, but you can. Hardly any trails around here have jumps.