Everyone can get into Kelp to purchase food. The amount of NP you have on hand doesn't really matter.

In order to receive the avatar, take home a food item, which won't always happen. You might have to eat there more than once to get a chance at taking something home. It's also suggested to have your pet as bloated as can be before eating. 

you can only pick one type of food to eat in every each course... and only one of that type of food. So you can have a max of 4 items to eat. The two cheapest foods, as of this post, are as follows:

Lemwart Fizz,
Thornberry Brew, 

They are both found in the cocktails section, and you can pick one or the other.

Therefore, you would need at least 7,000 nepoints with you in order to get the cheapest item for your pet to eat. However, there is not a huge chance you will receive leftovers if you only order one food. Generally speaking, you are more likely to get leftovers if you order more food.

Remember, you get leftovers (and the avatar) RANDOMLY when eating there. This means you might need to return and eat at the restaurant more than once before getting the avatar. 

Info from http://avatar.starried.net