To the Sea why not by Plane ?
After a couple of days in Tbilisi visitors want to see the Greater Caucasus and often also the Black Sea. To Batumi its about 400 km and takes by car 6-7 hours, by train even 12. But now you can be there in just 1 hour with Georgian Airways and it cost not more than $25. See the details at Georgian Airways http://www.airzena.com/main.php#results
The flights are operated daily 7.30 am to Batumi and 4.30 pm back to Tbilisi. Just enough time to jump in the water.