Radio, TV and newspaper are NOT the answer -- they reach too broadly, and thus 90% or 98% of the audience you're paying for will NOT be close enough to use your services.
Cable TV is an option, if your local cable outlet allows zip-code-specific targeting (but I'm not sure it would be cost-effective).
More practical solutions:
- direct mailing; either to all households or, more appropriately, buying lists that target the households you think are most likely to be clients; the total cost is likely to run from 30 cents to $1 per piece mailed, depending on what you send and how you send it.
- coupon mailers; you pay a much lower cost to have your coupon included in a bundle with others; there are several formats, with widely varying effectiveness.
- join your local chamber of commerce, and perhaps the "newcomer's club" or welcome wagon; perhaps other civic groups or "referral groups"
- Why exactly can't you have a sign? Is this a negotiation with the landlord? city regulations? Option: can you get permission to put a "sandwich board" sign out on the street corner for a limited period? Or some other temporary signage? How about marking your SUV or van with your dental practice name, and parking it on the street, or visible from the street?
- there are a zillion other options. good luck