1st DUI in 2009.Arrested June after 'anonymous' call. I had not been drinking. I refused testing. Offered plea for reckless????

Trial is always risky. This is your decision, and none of us have seen the evidence against you. Talk to your lawyer.

Hard to tell, without looking at the other facts and observations, whether or not your case is worth taking to trial. Reckless is definitely more favorable than a DUI
Conviction. Talk with your attorney!

If you were not arrested on the night of the alleged DUI, the State's case is not as strong as it would be if you were arrested on the night in question. Typically, a DUI charge with a lack of evidence may be worked out for a Reckless Driving conviction to avoid the associated penalties. An experienced Criminal Defense Attorney can help you navigate these issues and consider what is best for your case.

After all the years defending thousands of DUI cases, I'm still puzzled when I'm told by clients that they had nothing to drink, yet refused breath testing after arrest
If the State is willing to reduce your charges to reckless, they must feel they have a weak case. A lawyer representing you is best suited to speak to that since I don't have access to any of the police reports.
A prior in 2009 could put you in a mandatory jail scenario, and maybe a 5 year license revocation, so a reckless may be a good option for you. Talk to an attorney. If you don't have one, get one.
Good luck.