The Vita gets great reviews here if you mom likes that one and it fits. I don't know its specifics but many here do.
I agree with AdelaaR that $1000 is not needed for just casual riding. I have a Trek 7100 WSD (women's) but the Trek 7000 or 700 (WSD) would be good possibilities too. These are in the $400-ish range. Giant also has some models that are a little less expensive such as the various Cypress W models. My neighborhood is hilly so I needed more gears and chose the larger 700c wheels, but for riding at the beach, either the Trek Navigator or the Giant Sedona (both of these have 26" wheels instead of 700c as the previous bikes do) might also be good. There are different models of each and I think they come with different gear choices. Check out their websites to see the specifics on these. All these are classified as hybrid/comfort bikes. Both manufacturers also make beach cruiser models. It's my understanding they are heavier and don't roll as easily but are OK for level riding. The websites have a lot of info on each model. Personally, I think one of the comfort hybrids would be better (more versatile) than a cruiser but that's just my preference.
I'm not saying Trek and Giant are the brands to choose; they were the only brands available fairly close to my location so I chose from those two. I went with Trek because that shop was much more welcoming and helpful, and offered better service perks with a bike purchase. They were also the only shop that had a bike in my size after a month of looking. If the shops will let your mom ride the bikes (and they should), that would be good. I think the components are fairly equivalent at these price points. I obsessed too much over frame material and whether to get a suspension fork or not, and now don't think it matters much at all for just casual riding. If she likes a bike and it fits, it should work fine for her rides. If she is ever riding on sand, though, from what I've read, she would want a bike with tires at the wider end of the range. Others here are more knowledgeable and will hopefully offer suggestions as well. Any of the hybrid/comfort bikes I mentioned are good for pavement and smooth bike paths.
She should be able to get a nice bike for under $500 or so. The accessories I wound up getting are a floor pump, basic helmet, basic bike computer (speedometer/odometer--fun!), and a small underseat bag for my ID, cell phone, emergency cash, patches, etc. (The one I got was an Avinir Big Mouth, size small, for $10 on amazon, but there are many others available in many sizes.) I also ordered a "Road ID" bracelet which has my emergency phone contact #'s and medical info.
I bought the pump, helmet, and bike computer when I bought the bike, and they installed the computer at no charge and did a much neater installation than I could have done. Oh, I also had them install a kick stand. My bike didn't come with one but some of them do.
I'm 64, hadn't been on a bike in decades, and am loving my casual rides! All the best to your mom. Keep us posted on what she decides.
If you have more questions, the people on this forum have been fantastic to me!