As someone who happily travels solo, leave your wife at home - you'll be happy travelling, she'll be comfortable at home!
As for first trip, my first was to France with a side trip to London.
Having done some travelling since then and if asked to recommend, I'd say go to Scotland. You can spend a few days in London if you fly through LHR to see some of the sights there, then head up north. It's gorgeous, friendly, and fun to explore.
Where exactly you end up would depend on your tastes - the major cities are great, and the small communities are just as fun. I especially loved the Orkney Islands. Plus hey, distillery tours? Oh yes please!