A few things to consider:
Tip Over Bars: Strongly consider getting these for your Connie. The mirrors, footpegs, and side/front fairings will thank you.
About the driver pegs: If the previous owner hasn't done this already, you'll note that they only fold up about 45 degrees. this can be a problem if the bike goes over. I found it helpful to grind off the 'tab' on the footpeg that keeps the pegs from folding up completely, so that is rounded off and the pegs can fold completely up. This may help save the peg if the bike goes over (unless you already have tipover bars).
Handlebar vibrations: If this is bothering you, do a forum search on various solutions to this. This is a well discussed topic. I went with packing my handlebars and getting gel grips myself, but there are several good ways to address this issue. This might also be a good time to think about bar risers...
Front Fork Brace: If your bike doesn't have one of these already, consider getting one. Again, forum search is your friend.
Visit SISF's site: His carb kits, overflow tubes, and '7th gear' unit are da bomb! You may find something you like there...
https://sites.google.com/site/shoodabenengineering/Also, Murphskits: Great source for various things for the Connie:
http://www.murphskits.com. Great service as well!
I love Bergman's quick release tank kit! This makes accessing the plugs/valves just a little easier. Murphs sells these.
TCro and Snarf have some nice things for the Connie too (Stick Coil kits, new shift linkage, etc.). See the 'For Sale' subforum for info.
Bafflectomy: Do a forum search on this topic, and make up your own mind. Doing this lowered my handlebar vibes just slightly, gave me a slight boost to performance, and most importantly: My Bike Sounds Meaner Now...