The famous dishes of Guilin do have relation with meat, such as roast pig, chicken and duck. You could have these dishes at any restaurants of this city. On the other hand, it is more interesting to try the local snacks which could be found along the road or street. Finally, please don't forget to have the well-known Guilin Rice Noodle.

As for visit, the first one should be charming Li River. You could take a cruise along the river from Guilin to the exotic Yangshuo town. This town has attracted a large number of travelers for its beautiful rural life. As for details, please read the introduction on Guilin and Yangshuo firstly:
https://www.travelchinaguide.com/attraction/guangxi/guilin/
https://www.travelchinaguide.com/cityguides/guangxi/yangshuo/