You could try cleaning it with some of the filters available for Audacity
. There's not much (that's doable) you can't accomplish with Audacity. And it's free for the download.
I've never tried doing what you want to do with it, although I do
use Audacity for a lot of other things. Look here
for some ideas to get you started.
The real challenge is going to be the somewaht random character of dining room noises. That makes it difficult to filter them out without also removing things you'd rather not from your audio source. The best you can probably do is get rid of enough of the sounds that make you want to scream so that your recording is at least tolerable to listen to.
One of the mantras of the recording world is: "Don't try to fix it in the mix." Which is to say, getting your original source as good as you possibly can is 90% of achieving a good recording. So if you plan on doing a lot of recordings in environments like the above, look into getting a standalone portable recorder (sometimes called "field recorders") with noise suppression features such as musicians and news reporters use. Tascam, Zoom, Sony, and all the usual big names in audio make them. Not cheap. But what price do you want to place on keeping your sanity?