I used to cruise a lot before we got a place in Panama. Nowadays, not so much!
Cruising can be fun. Check out Cruise Critic for sure. They sometimes have meetup groups for each trip, so if you're mom is going alone, it may be a way for her to meet up with other people.
Also check for shore excursions where she's visiting. And she should always be early back, never late ( Cruise sponsored excursions are the only ones that can be late. You go on your own, they can and will leave you sometimes if you're late!) One more thing about her visit, get her a insulated camelback eddy or a Hydroflask and fill it with water and ice from the ship. Not knowing her health situation, its best for her to drink from known water sources.
Personally I like and have a few Hydroflasks because they really do hold their temps and they're relatively inexpensive
https://www.amazon.com/dp/B01720CDTG?psc=1
She should keep a copy of her passport on her person whenever she's off the ship. No need to take the real thing, a copy will do for ID purposes.
Mosquito repellant. I do recommend one with deet.
Sturdy walking shoes. Keen has some amazing sandals that cross the bridge between casual and hiking (and some dry super fast)
http://www.keenfootwear.com/sandals
Depending on her energy level and excursions, they're worth it (I use mine pretty much every day though

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Also, a walking stick. I know passe right? but again this is your mom. if she's doing any type of excursion that involves hiking or walking/hiking, YES get one! I have 2, I used mine a lot when I hiked with my dog and also in Ecuador. Some of the excursions when I cruised warranted having at least one of them along, and it closed up well enough to fit in a suitcase (or easy enough to hang on a backpack!). The extra added benefit, you can beat the hell out of somebody if they mess with you...just sayin!! Mine are aluminum. No need for some old lady looking thing right?
https://www.amazon.com/High-Telescopic-Trekking-Walking-Climbing/dp/B0140GSYFW/ref=sr_1_3?s=sporting-goods&ie=UTF8&qid=1473776332&sr=1-3&keywords=Hiking+sticks
If she's island hopping, cash is king, take plenty. I make sure to have lots of ones especially. She'll have a safe in her room so she should not carry too much with her everywhere.
Most cruise lines either do auto gratuity, which I recommend if Princess has it. I do auto and leave something extra for the folks that clean my room.
On the ship they will have plenty to do. Many have a gym, sometimes some classes like yoga or spinning. There's a pool (but I'm not a lounge by the pool type person) Also, early A.M. is one of the best times to get up and take a walk around the boat. Not sure what her ship will be like but most have a jogging path on the upper deck.
Then there's some deckside games too.
The after dinner shows can be lots of fun depending on what they have. And yeah I played bingo on the ship (I didn't win but is that really the object??)
As said, wash hands, sanitize, take it SERIOUS! and yes, if she has her own lysol, even better, and I'm not even a germophobe! Noro is nasty as hell, it can really take a lot out of you so yes, this is where she needs to really be careful and wash her hands a lot. There will be hand sanitizer all over the ship, but she should have her own for off the ship times.
I also carried small pack of travel toilet paper (hey, ever have to use the toilet in on a small island? yeah worth it!!

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