Time Trialling
This is for loonies!! People who like a bit of pain. It's all about testing yourself against the clock over a set course and distance. What other riders do is irrelevant (well, almost). If you join a cycling club the chances are they will offer time trial events and I would certainly encourage you to have a go. Whilst I no longer participate (for me it's a case of been there, done that) there is no doubt that there is an almost addictive element to riding time trials. I was probably riding as many as 4 a week and enjoying every minute.
There seems to be a bit of a divide between road racers and time triallists. Personally, I can't see why you can't enjoy both. Anyway, time trialling is fun, in a weird and painful sort of way.
Your local club will, almost certainly, run time trials throughout the summer. They will be on a variety of courses, some flat, some hilly. Being a member of one club should allow you to ride in other club trials too.
Living, as I do, in Cumbria some of our courses are spectacular to say the least, like the course along the shores of Bassenthwaite Lake and in the lea of some fantastic mountain scenery. Trouble is, if you stop and look at the scenery it does nothing for your time!