Havasu doens't have notable 'trails' as much as just square miles of roaming available. One area well known is 'Bison', as that's the name of the paved street that takes you to the dirt. That eventually leads up to 'the waterfall' which is mild (2wd) up to the falls, and then moderate thereafter. No winching needed, nor lockers if'n you aren't afraid of the skinny pedal. South of town, is more roaming in the 'Standard wash' area. Head south on 95 about 3-5 miles, and look for a small quarry operation on the left. The whole area to the left of the highway is open game. Like Bison, there are short trails interspersed wtihin the general riding area.
Further south towards Parker; try Bill Williams River area, you can play in clear water crossings, and more mild wheeling unless it's flooded then it's very muddy. Nearby would be Vampire Mine trail, which is the beginning of the more technical trails found in the Parker area. I'd recommend the Parker area for it's more established tough trails. This is where the magazine guys go when they come to the area.
North of Havasu is Bullhead City, and Sleeping Princess (never been), and NE is Kingman with the Hualapai Mts, and "Flag Mine Rd" just off Hualapai Mt Rd. Turn around at 'Wild Cow Springs" unless you plan on going the rest of the 35 approx miles offroad back around the mts to Yucca on I-40. Very mild, but scenic trip. Unless you know where you're going in the Hualapais, stick to the easy trails, as the terrain makes for harder orienteering than the low deserts. 15+ degree temp diff. along with decent tree cover makes for a nice home for elk, mule deer, big cats, etc.
Happy wheelin' !