Las Vegas is a marvellous place for a low-hour pilot to build experience. True, the airspace is busy, but your checkout will take care of that. Generally flying there is far easier than the chaotic UK. Assuming you rent at VGT (North Las Vegas) or Henderson, your checkout will probably take you out over Lake Mead and will certainly involve the proceedures for leaving and re-joining the Las Vegas class B airspace. (Actually you don't have to enter the B at either place, but it's an essential plan to get checked out in it).
I should budget for a little extra time with your instructor so that the experience can be more relaxed - as it is, you will be combining a BFR (needed for your reciprocal licence) with the checkout - say 2 trips, one of which could be a cross country (see if they'll let you go to Temple Bar, a dirt strip out by a Marina on the Lake), and 2 Hrs of ground. I'm sure whoever you rent from will have their own policies regarding experience, etc., so don't be afraid to ask them.
I started flying there on a reciprocal licence many years ago with similar experience to yours. For a long time I limited my expeditions to about 150m from VGT, which takes you across the Lake (which you will know from your checkout) and about 1/2 way down the canyon toward GCN. I did that a few times, besides other places like Death Valley and Lake Havasu, before venturing all the way to GCN itself, which really requires an overnight if you're going to visit the village.
All my early flying was solo, and in a 152, and you can certainly get to the 11,500' needed to cross the Canyon through the corridors solo in a 152 in January. Speaking of January, it can be a superb time to fly. This year for instance a permanent high pressure gave continual clear skies and light winds throughout the SW. But in other Januarys I've seen howling gales, ferocious sandstorms, driving rain and mountains of snow - all of that in Las Vegas! So there's an element of luck involved at this time of year. (But in 20+ yrs, I've never been there in the winter and not been able to fly).
So starting a US flying career in Las Vegas is a really good plan. Be cautious about how much you plan to do initially and especially about how many, if any, passengers you take. There are dozens of places within easy reach in 3Hrs fying (many FBO's require 3 Hrs per day) and if you do go to GCN, plan a couple of days over it and don't be intimidated by stories of hectic tour traffic which while obviously well meant, don't really apply to the winter. Happy times!