You really shouldn't tan at all if you have tattoos because it will make your colors fade really quick, but if you insist, I would wait at least two weeks after getting anything done, and make sure you cover the tattoo with high spf sunblock.
if its around the tattoo your just received then you should wait till the first one heals....otherwise it doesn't really matter....i'v gotten 4 tattoos in one week before...just be sure to keep them...
I recommend waiting at least one month (preferably three) if you must tan. This gives time for the ink to "settle" into your skin, and your skin to heal. However, exposure to sunlight and UV rays...
I would suggest at least a week. Remember your new tattoo is an open wound and crap will get into it possibly leading to infection. Plus if you're going in a swimming pool with chlorine you will...