You don't have to have a bad motorcycle to have a cheap motorcycle. Even new motorcycles can be good in a number of ways without compromising on everything.
Of course if you are willing to compromise in one or more area's then you can pick up something pretty unique.
What about size? You could always get a mini motorcycle! OK, that might appear a joke to you but they fill a niche for some people.
If age is important and you want a brand new one, well how about a Harley Davidson 883? It's becoming more famous because of it's cheap price more than anything else, under $7k for a brand new Harley is quite the headline.
Willing to compromise on engine size? The larger the engine generally the more comfortable and balanced the motorcycle is, that's what they are preferably to touring motorcycles and choppers like the Harley Davidson Rocker. But small doesn't mean useless. I'd recommend going down to a 125cc motorbike if you are not doing many highway miles. This size engine is great for around town riding, and is much easier on fuel consumption too and doesn't have the annoying noise like a 50cc scooter.
Second Hand Cheap Motorcycles
Of course the most common thing people compromise on is age. You can make great savings on a 1-3 year old motorcycle compared to a new one, just be sure to verify it is of good quality and hasn't been in an accident or has finance due on it.
I'd advise checking out the motorcycle before committing to purchasing it. Your local advertisements are the best bet to find a cheap motorcycle. Newspapers, craigslist, gumtree, and even motorcycle dealers.
If you have a specific model in mind type 'MODEL NAME enthusiasts club' into Google and you should find a forum with a for sale section, you will often find the best prices for your desired motorcycle here, and have the option to negotiate cheaper too.
eBay is a last option but you should really check what you are buying before bidding, and if you do that many sellers will be happy to negotiate outside of eBay.