How do I keep a bike feeling "new"?
Aesthetically, it's just a case of keeping it clean. Use a toothbrush to clear accumulated dirt out of the little nooks and crannies, like the joints between tubes (especially around the bottom bracket). Waxing the frame can help keep that brand-new lustre.

The back of the chainring and spider, sprockets, rear hub, and dropouts, can get grotty pretty quickly, so use a gentle degreaser to keep on top of it. Same for the chain. Use a brush to get all the little bits of road dirt out of the links, then, with a clean brush, apply oil liberally. Brush it right in there. Wipe off any excess afterwards. As far as the feeling of mechanical "newness" goes, a clean, well-oiled drivetrain is the biggest contributor IMO.

Edit: Bike cleanliness pr0n