For good budget diving + beach, the Yucatan is an option - Cancun, Playa del Carmen or anywhere along the Maya Riviera (Akumal, Tulum), depending on what level of development you prefer
Cozumel is of course the nearby premier dive destination, but your wife needs a beach -- for these same reasons (my wife is also a non-diver, budget), we chose Cancun & PdC for our last vacation. Both areas have nice beaches. Also, if you have extra days, you can visit ruins (Chichen Itza, Tulum, Coba, etc) or swim (or even dive) in the cenotes
Airfare has been cheap - We paid $450 round trip per person from Oakland in Dec. And you can always find budget lodgings throughout the Maya Riviera. There's also a lot of vrbo (short-term rental of individual homes/ condos, etc).
I only had I day of diving each in Cancun & PdC -- although it was more advanced diving. The marine life at the Cancun sites were especially nice - hopefully its the same at the OW sites. I cant really comment accurately on PdC diving (I didn't have great dives, but maybe due to other factors), but the beach and the town is much nicer than Cancun. I noticed in both locations there was a lot of certifications going on.
I would also plus one on Hawaii being an option, if flights are cheap from Wash, although lodging & food will be more expensive than the Yucatan. The diving Ive done off Oahu was very good. If you want to get away from Waikiki you can get a vrbo elsewhere on the island, as there are no hotels. However, if you do that, you'll likely need a car.
Hope you enjoy your certification!