Hey Tomb those are great bikes. I just sold a "AN" dated Breeze last fall, a yellow one.
Yours is Sky Blue, btw. The tires are available through Niagara Cycle if your LBS can't locate some. Blackwall or Gumwall, those are your two options. I have a spare single probably if you can't find any anywhere else. The deal with the rims is, Schwinn's S5/S6 standard was a little bigger than everyone else's 26x1-3/8" lightweight tire, and it's become the less common size. You need tires with a 597mm bead diameter. If you find tires marked 590mm, they will not work.
They are sold as Pyramid brand, or Kenda, or IRC (Indonesian Rubber Co, lol). Niagara lists them at $12 apiece or something close to that. Memory Lane carries them as well:
http://www.memorylane-classics.com, also great ppl to deal with. They KNOW what you're talking about when you call.
The SA shifters are simply held by a clamp. The one screw thru the plastic cover, with a deep nut from the back holds it all together. Careful with the covers, they do crack easily. I've found them NOS on Ebay for as little as $3 if you break yours... I bought a few extras. New cables for the shifters are available thru those sources as well, and new ones come apart with a lock screw at the back end, vs original style that can't be disassembled (Schwinn SA cables are crimped on at both ends, not fixable). New ones are less than $6... hit me up if you have trouble finding one.
The position of the clamp on the downtube of the frame is important to the whole thing working right. Make sure it goes back where it was if you remove it for cleaning. Likewise the pulley wheel down by the kickstand. Both of these have a sinlt clamp screw too. The cable has a split bushing in the downtube clamp- don't lose it, it'll stick to the cable probably when you take it apart but then fall off and get lost when you don't expect it. It's that white thing the cable goes through and I've lost a few of them over the years.
Note that rear hubs have pretty fragile left-side nuts, and can be stripped by overtorquing, and it's a fine English size thread, a special nut. Nothing else fits it. New ones are only a couple bucks but I've seen more than my share get stripped out. Don't try to thread anything else on there, it's not gonna work and may screw up the axle. Use sewing machine oil or 5W or 10w oil in the fill hole- a few drops probably all thats' needed to keep the hub happy. NOT 3-in-1 oil, that's a vegetable base that will gum it up eventually.
Other parts are straightforward Schwinn, common to everything from Stingrays to Suburbans... one piece crank, Weinmann brake calipers (get modern pads, trust me!). Expect a stuck stem bolt or clamp- loosen the top headset nut if you encounter this and get oil all down inside the stem. Had a lot that were badly stuck till I tried that trick.
Last, be real careful around that chainguard silkscreen- they like to come off in your hand when waxing the paint.
Good luck, have fun with it, I'm sure your wife will enjoy her new ride! If you need anything for it, shoot me an email, I've had lots of Breezes and their relatives over the years. Lots of parts.
--Rob