A warrior or stock 172 can make it in the mountains in good conditions, but it's not recommended, especially with no experience. A 180 HP converted one is better.
The service ceiling in a 172 is just over 14000 in density altitude. Passes in the central Sierra are around 10,000. That's close in summer, especially if it's windy. Note that the XP and RG models are different. SP's are not (heavy).
I'd consider flying with you, but somewhere a bit tamer first. Unless this is your 172, there are going to be issues of rental rules. A 172 is adequate for Tahoe, but not Mammoth.