Hi, you could travel in Guilin easily by yourself if you are an experienced back-packer. This city is really an ideal place for hiking. However, if you would like to the suburb such as Yangshuo and Longsheng from Guilin, it is suggested that you participate in an one-day or two-day's group since the public transportation (mainly depend on coaches) there is not so satisfying, especially in those remote area. Of course, you could find some back-packer there.
PS: I found some good self-help tour in Guilin at this page https://www.travelchinaguide.com/package/guilin.htm

During the summer August, Guilin is somewhat hot, sometimes may be muggy due to the rainfal. But, please take it easy, it is still comfortable for traveling. And, most of the places are safe enough.