Hey Danna! First of all welcome to Reno! Depending where you're moving from it might be quite the shock! At least for me it was...I'm used to lakes, forests and green!
There are options depending how much you want to commute and spend on $$$. We currently live in North Valleys (Sky Vista deveploment, Stead) and we like it out here. It's about 15 minutes north from downtown, nice and peaceful with tons of walking trails, a big regional park with baseball courts, soccer field, playgrounds etc. Grocery stories (they're building a Walmart here too), library, post office etc are only a few minute drive away. You can get more for the money here. Look for the newer side of Stead though. Older side is a little sketchy.
Northwest Reno is nice as well. The older side doesn't really have all that many parks and it's surrounded by big roads. Newer side can be $$$.
Old SW Reno is nice but houses are small and $$$$ and yards aren't huge either.
Also, look for Spanish Springs. Nice residential area with big yards. You can get more bang for your buck there than in NW or SW.
Also new deveploment in Cold Springs is nice. It's very peaceful because it's kinda out there but many people say they like it there. There's a new YMCA there with different activities for all ages
I hope this helps!