no... not all cell phone has ans machine. it depends on the plan and service provider and the deal she got at the moment...
keep it cool and try calling her again, but don't keep calling all the time. she will freak out and maybe run away. she may be busy or the phone is out of battery or just left it somewhere and forgot to bring it with her. and don't contact her other way if she didn't give you the info (ie: don't call her home if she didn't give you the number). otherwise she will think you're stalking her and run like crazy
if you know her place, why don't you make yourself "just hanging around the neighbourhood" and stop by her place?
as to where to take her out.... depends on what you think she likes to do (i assume you two have talked about some of your interests). decide where to go from there
good luck

-496-