Brenda
For a 4 week stay you "should" be allowed thru under the 3 month visa waiver scheme (you should check US embassy website if you have any criminal record).
www.travelcitydirect.com are usually pretty good - but with only 4 weeks you could pay top prices (you want to book 6+ months for best deals).
or, do a Google on "flights to the usa" and try each website for bext deals.
Paul