Hi, hope you will enjoy being in Lebanon, its very nice and weather now is very good.

According to what you are asking:
MEA (middle east airline) has direct daily flights to beirut, it costs arounf 1700/2000 QAR. www.mea.com.lb

Hotels, you may find a lot of Boutique Hotels in Beirut, especialy in Hamra Street. (check below link for hotels in hamra street (prices vary between 50 USD and 150 USD per day)

http://www.hotelsone.com/landmark/lb/hamra-street.html?as=g&aid=22989710...

Other expenses are normal, and there are lot of varieties.

Sure you have to visit Beirut Down Town, Cornich, Zaytouna Bay, Jouneih (telefrique, & Harissa), Jbeil (byblos and old Souq) and lot of places.

Please don't hesitate to ask back for any additional things.

Again, have a nice trip