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First go through this tutorial for getting familiar with
Android Google Maps and this for API 2. -
To retrive the current location of device see this answer or this another answer and for API 2
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Then you can get places near by your location using Google Place
API and for use of Place Api see this blog. -
After getting Placemarks of near by location use this
blog with source code to show markers on map with balloon overlay with API 2. -
You also have great sample to draw route between two points on map
look here in these links Link1 and Link2 and this Great Answer.
After following these steps you will be easily able to do your application. The only condition is, you will have to read it and understand it, because like magic its not going to be complete in a click.