First, kudos to you for taking charge of your health! Too many of my friends' lives depend on eating out and drinking wine as the major focus of their social life and entertainment. They are obese and have a "sticky relationship" to alcohol, but blissfully continue (except one woman who got a diabetes and liver disease diagnosis).

No reason you can't continue to invite these friends, drinks and appetizers are especially easy make LC with very little effort; cheese, charcuterie, nuts, olives, hummus, veggies, sparkling flavored waters. Add in pita chips and drinks for them.
But as Robin said, you may also want to find friends with healthier habits...there are Paleo and Low Carb meet-ups and support groups around here.

To be fair, you have admitted restarting many times. Reading your thread titles since 2007, you have also quit drinking other times. Maybe these friends have heard it all before? Maybe it is time to read a low carb book to help you find a plan you can really stick to. Do you start drastic changes in your diet abruptly?..maybe a more gradual reduction in carbs would work for you? Consider the new South Beach gluten free plan or other lower carb solutions. Check out a few LC diet books from the library and decide which would work best for your personality.
If getting rid of all carbs at once is better, then follow only one plan to the letter. THe Atkins Induction plan in the sticky or the VLC plan in this free handbook works well, https://healclinics.com or the version of same diet in the very helpful and recommended Why we get Fat book.
Think of other ways to change your habits permanently. There are practical tips on Eating and Exercising in this thread:
http://forum.lowcarber.org/showthread.php?t=468195