If you'd consider buying used, take a look at a PeaveyT-40 bass. Made in the USA from the late-seventies to the mid-eighties or so, built like a tank, tone to spare. This is a 4-string bass that you can pick up for around $200-$250. The only problem is that it's extremely heavy, which could be a problem for gigging.
Another good (used) bass is the Ibanez Roadster or Roadstar.
Either of these would give you a professional-grade used bass for the price of a new entry-level instrument.
If you absolutely want new, I would tend to agree with the Ibanez and Yamaha suggestions made above.