Hi Rhonda,
I was able to take my first solo trip to WDW last fall. It was so much fun that I have already started planning it as an annual trip. I have never been to Europe, so I am unsure of how the group tables work there, but I can tell you that there are no community tables at the Disney World restaraunts. The only exception to this is at Teppan Edo. This restaraunt, located in Japan at the World Showcase, seats the guests around a grill where your dinner is prepared. The grills typically fit parties of eight and parties will be combined. This is a great location to meet new people and dine with others.
There are a number of locations where you can dine at the bar, for example Rose and Crown in Epcot, ESPN at the Boardwalk resort, and Rainforest Cafe at Animal Kingdom and Downtown Disney. There are also a number of restaraunts that feature open designs that allow the guests to view the chefs at work. Examples of these include Mama Melrose, Portobello's and Flying Fish Cafe. One of my favorite locations to dine alone is Tony's at Magic Kingdom. I request an outside table and enjoy watching the crowds. Depending on the time of your reservation, you can also enjoy the passing parade or the flag retreat ceremony. You can find additional dining information
here. Remember to make advance dining reservations by calling 407-WDW-DINE or 407-939-3463.
Hope you have a fantastic time. I love traveling with my boys but a solo trip to Disney World is something to treasure. Enjoy!