Whether you already have a nice patio table or want to make your own, now you can learn to make your own (or hack your existing table) thanks to this great tutorial by Remodelaholic. The article is incredibly detailed so you can really get all the instructions you need to do the work for yourself.
Switching the chest out once the whole thing is complete is pretty simple, so even though it's not included in the DIY article, you can always consider switching out the boxes for planters so you can have a living floral centerpiece in your table.
Read more about the project over at Homes and Hues: Make Your Own Patio Table With Built-In Ice Boxes