You can easily arrange everything in Huaraz. If you have it, it's best to bring your own equipment (think about boots, harness, axe (and, should you plan something harder, a second tool), sleeping bag, inflatable, tent, stove). The primary reason is that while all the agencies in Huaraz will provide all the necessary gear, the boots might not fit you well and it's not guaranteed that the gear is top notch. Since you're going to travel for a longer period, I assume that you were planning to bring most of this already. And while they'll provide the gear, they may charge something for it, or give a discount if you bring your own (do ask for that if they don't mention it).
The agencies themselves can give you lots of good information. You can pop into several offices and ask around about which climbs are possible and what it would cost you, either joining a group or just for the two of you. In addition I recommend checking in at Casa de Guias. Sometimes there is a mountain guide present that has good information. If there isn't, you can always ask when a guide will be there, so you can come back later. The difference is that the agencies obviously want you to book with them, so they have an incentive to paint a more favorable picture, while most guides usually don't think about business opportunities but just share their knowledge.
The climbing season in Huaraz starts more or less in June. Some routes tend to get in shape a bit later, others earlier. If you arrive by early May, you can always explore the Cordillera Negra, for that's possible all year round. No guide needed at all. If you like rock climbing, do go to Hatun Machay for a day, or two. Even if you don't, just visiting for a day and hiking around is worth it.
Andean Kingdom, one of the agencies in Huaraz, organizes cheap transport, operates a simple refuge up there and offers rock climbing instruction. However, when I went there myself, I saw an instructor explaining things for a couple of hours to a group of novices before they finally got around to climbing something, so I wouldn't recommend their introductory course. For novices, I believe that the best way to learn and keep it fun is to make real sure that everybody knows how to belay their partner while top roping and then start climbing. I mean, with bolted routes it's a waste of time to teach novices how to use stoppers, cams and so on, right?
A small section of the rocks at Hatun MachayYou can also go hiking in the Cordillera Blanca or the Huayhash. If you have a bit of hiking experience, you don't need a guide for that. A much cheaper option is to hire an arriero with a few mules (or even horses). The mules can carry your stuff, and the arriero knows the routes. Even the mules do. If you want to make it even more relaxed, you can consider hiring a cook as well. Mind you, if you just hire an arriero, you'll have to do all the shopping ahead of the trip, do all the cooking, and provide shelter and food for your arriero as well. If you hire a cook too, you can arrange that he not only cooks but also does the shopping and brings a stove and fuel. Just make sure that you don't end up at your first camp at the end of the day to discover that you've forgotten something important. For all my trips in the area I always did the shopping to be sure that we had everything.
Which peaks are in shape depends on the amount of snow that will fall between now and your arrival, and on the weather by the time you get there.
Urus Este,
Ishinca,
Vallunaraju and
Maparaju may very well be possible, to name a few. Guided parties with people that have no previous mountaineering experience regularly climb the first three of these. Maparaju is rarely guided, but is real easy too. Three additional candidates are
Pisco Oeste,
Huapi and
Yanapaccha. I wouldn't recommend any of these as the first peak, but if the first climb has gone smoothly, you could consider them. Of these three, Pisco is easily the most scenic, so if it's in decent shape, by all means go for it. For your reference, Yanapaccha is a bit harder than Huayna Potosi; all others mentioned, including Pisco, are easier, at least a little.
As for higher peaks in the Cordillera Blanca, i.e. 6000-ers, I wouldn't recommend any of those to someone without mountaineering experience. Should you want to try climbing one, it's best to first ask around in Huaraz about route conditions. That said,
Tocllaraju is one of the easiest ones, relatively speaking. It's still not easy though, and a big step up from Huayna Potosi, but if the route is in good shape, then, after acclimatizing on the likes of Urus Este and Ishinca, with a guide you could consider it yourself. Then again, if the snow hasn't settled properly yet, which is what I would expect in May, the avalanche risk on Tocllaraju could be too high. On the other hand, since your girlfriend has no experience yet, it's probably too steep a learning curve for her anyway. I mean, with a guide it won't be unsafe to try it, but whether she'll be able to cope with the steep sections, and whether she likes it, that's a whole different matter. To put it in perspective, once ice axe isn't enough, you'll want a second tool on Tocllaraju.
In 2011, the crux on the Tocllaraju normal route was to get on the NW ridgeIn the past,
Copa used to be a relatively easy 6000-er, technically speaking. I haven't climbed it myself, so I can only echo what I've learned from other people, but it seems that getting on the glacier has become a lot harder over the years, and that's probably the crux now. But how hard it really is, I couldn't say. The glacier itself is big, but not nearly as steep as Tocllaraju. Once you're up there, the main problem most likely won't be avalanche risk but the risk of hidden crevasses. And there may very well be deep, unconsolidated snow on the relatively flat but seemingly endless slopes. It takes time for the snow to consolidate, and in May and June you might need snow shoes or skis or you will simply be too slow. As before, you can ask around in Huaraz about the conditions.