Man, i went to Beyrue 10 times... I alawys rent an apartment, car is a must... if you go skiing(lot snow now) go to Mzaar, if just Beyrute, try any place close to Gemayzee (nicest bars and restaurants) or Asharafyeh.
Visit the lebanese restaurant in front phoenicia, they have singers and dancers, worth to go.
I have so many tips... i you need.
Regards