I've been to the top of most of the peaks in The Lake District - the view from all of them, particularly Hellvellyn is spectacular. I've also done Snowdon via several different paths (the 'Crib Goch' route is pretty hair-raising).
I also went almost to the top of Mont Blanc a couple of years ago by cable car - the views on the way up were amazing, then it got a bit blizzardy.
I've trekked up into the foothills of Annpurna and Dhaulaghiri in the Himalayas too - the scenery there is fantastic.
Ben Nevis has one easy route all the way to the summit but it was a bit misty when I got there.
All of these are do-able for anyone who is reasonably fit and none required any specialist equipment.
I usually pack some basic essentials in my rucksack: packed lunch, waterproof jacket, plenty of water, a whistle, a torch/map/compass, Kendal Mintcake :-) I would also recommend a GPS plus spare batteries, and of course - a good camera.
When taking on a mountain hike alone, it's essential that you check the weather, set off early, work out roughly how long it's going to take then inform the nearest mountain rescue post when your ETR will be.