Sounds like a few recommendations for accommodation, but I'll throw mine in for consideration.
When I was there I met a local surfer called Sato who was setting up a very small hostel. Probably think of it as a fancy homestay option. It was pretty run down when I was there, but he'd just moved home to Mancora after living in Indonesia for a couple of years surfing. He has done a GREAT job of doing the place up and I'd recommend checking it out. He's a great guy, and knows the local conditions (for surfing, anyway.) It's pretty well located on the main street.
https://www.facebook.com/taroland.peru?fref=ts
Another option is a more established hostel Casa Naranja. Cheap and good quality and great hospitality. Situated up the hill, it is a little less central than your other options, but still only a short walk.
Pretty much anywhere you choose to stay is within walking distance of the beach.
Can be awesome surf there. Or can be flat as. I had a bad season and only saw a couple of good days. But that is the nature of the beast. Wind was more reliable than the waves (Aug-Sep)
If you actually want flat water, you can get it at Organos. You can get there by bus, or hook up with a kite school. Good option for doing downwinders back to Mancora.
If you're chasing waves, you can get them in Mancora, but it is worth heading South to Cabo Blanquillo. Great atmosphere in this place, but you really will need to hook up with someone to get there. I highly recommend trying to get there if you can. Not necessarily the best conditions. But a beautiful spot to kite.
Or Lobitos. Definitely the best pick for the waves. The offshore wind and gusty conditions can be pretty unnerving. And the water is a damned site colder than Mancora itself. But far and away the best waves I've ever ridden. It is feasible to get there by public transport. But not recommended. It makes it a real mission. Much better to hook up with other kiters. The schools don't tend to go there regularly, but they will generally know who is heading that way.