Trevor
Never been there but blokes I've met whilst Bonefish fishing in the Caribbean raved about the quality of the Trout fishing in the legendary San Juan river - to the North West of the state.
Surprisingly for what I've always though of as a 'desert' state there're any number of rivers and lots of lakes - so, as well as the Trout, things like Largemouth Bass and Walleye would be on the cards. Lake McMillan, for example's not a 'million miles' from Lovington. As a starting point though you could perhaps try the state's official web site -
http://www.wildlife.state.nm.us/recreation/fishing/ - or alternatively try the 14 day free trial on this site -
http://www.trails.com/stateactivity.asp?area=14326.
Dave