from laguardia into manhattan should be $16-$26 dollars cab fare, you must add on any tolls or tips as well. it should take 20-30 minutes to get into the city from the airport, without traffic probably alot less.
always ask the airport workers for an authorized cab, dont just accept rides from anyone cause people will rip you off, and always be alert of your surroundings and make yourself blend in while walking the streets and on train stations, be street smart but also have fun and enjoy a whole new lifestyle while you visit nyc
theres tons of places to visit
chinatown you can walk the streets and buy off the vendors, they sell alot of neat stuff on the street, if you are not interested just say no thank you
little italy has alot of good places to eat and is nice to walk
central park is nice during the day as well
you can make a day out of the statue of liberty or empire state building too
greenwich village has alot of cool shops and bars, alot of weird punk/goth/sex toy shops too
southstreet seaport, times square, have fun