Put the word out with some local cyclists and groups and friendly shops (if you have), that you're looking for a good quality used bike for a reasonable price.

You can end up with some real gems, that still have an aura of quality and craftsmanship about them.

The Classic & Vintage forum here on bikeforums.net can give more clues about this appoach, and about other ways of finding these bikes.

Newer less expensive bikes just don't have the same sense of quality.

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Then use the extra money to buy some quality accessories.