For a kit lens, I was really surprised by the image quality of the 18-105mm VR. It is a fairly decent zoom range, the auto focus was always accurate and stopped down to f/11 it was razor sharp. There was some barrel distortion at the 18mm end, which is easily corrected in Photoshop but apart from that, I never had anything to dislike about it.
If landscapes are your favourite, then a dedicated wide angle lens is your best option. 18mm on a crop sensor isn't really 18mm. Its 27mm on a Nikon APS-C sensor, so going for the ultra wide angle lenses like the Sigma 10-20mm is probably your best bet. The Tokina 11-16mm f/2.8 is another fantastic lens but, they tend to go for around the £375 - £400 mark used, sometimes more.
For £500, like Matt rightly says, you'll probably struggle to get two decent lenses, at least at retail prices. I would suggest you look on eBay for a secondhand Sigma 10-20mm (£275-£300) of which there are two versions - a fixed f/3.5 throughout the zoom range or a f/4.5-5.6, or a Tokina 116 if you can find one for under £400.
You can also go a Nikon 55-200mm VR for around £100. Optically, its very good and extremely lightweight. Not the fastest to focus but, it should do a good enough job on the bike racing, although I would suggest you pre-focus on the track and then aim for the bikers, so that the focus doesn't have so far to travel/hunt.
If you were to get the Sigma for under £300 and the Nikon 55-200mm VR for £100, you could also pick yourself up a 50mm f/1.8D for about £80, which is an excellent portrait and general use lens. Razor sharp and has a wonderful shallow depth of field, allowing for some really creative effects. Reverse it, or mount it on a set of extension tubes and you have a decent macro lens too. The combination of all 3 lenses will pretty much cover all your bases.
Good luck and happy bidding