Well, with a ten person limit I certainly would have to have more than one dinner party! They'd have to be for different reasons, too... humorous parties, serious parties, a poetry reading party, a party at which I invite davem, Fordim, and Sauce and just let them talk while I scribble furiously on a notepad

.... but I digress. Here's what my first one would look like.
Going clockwise around the table...
1. Me, your gracious hostess, at the head of the table.
2.
Fea, a great and very funny person, would sit to my left. We'd discuss art and then share some pictures after dessert.
3.
Elrond would have to sit nearby, and share with us some of his wisdom. We'd keep things from getting too dry by convincing him to let Fea and I wear his tiara -- whoops, I mean
circlet.
4. Keeping to boy/girl/boy/girl pattern, I would then seat
Child of the Seventh Age. She seems like a wise woman to me, with whom we could certainly have some deep conversations.
5.
Meriadoc Brandybuck, a charming and intelligent little fellow, would be next. I'd like him to come because everyone needs a hobbit around to add some cheer.
6. Next,
THE Ka. And she's not just
any Ka, mind you. We'd discuss mystical things and compare star charts.
7.
Grima would have to attend, because I have a feeling he never gets invited to any good parties. Being a blonde, Nordic-looking female, however, I would not place him too close to myself. Later I'd get him a couch to lie on, don some glasses, and ask him age-old questions such as, "Did you really
love Eowyn? Or was it just, you know, physical attraction?"
8.
The Saucepan Man would be the next seated, disrupting the alternate male/female placing, but also providing protection from any villainy Master Wormtongue may have planned. Any fast moves and Sauce could wallop him on the head with a pan -- not
too hard, though! Sauce and the next guest would certainly drum up some interesting conversation...
9.
Fordim, a scholarly gent with a humorous streak, would add both wonderful attributes to the discussions.
10.
Maglor would sit to my right; we would discuss music and probably bore the pants off of everyone. Perhaps he'd perform for us later in the evening.
As for the food... ehh, I'm not much of a cook -- hope you guys like White Castle! I'll make some cakes, though, for dessert...