I am thinking of getting some project management software as a present for my mom. She manages various rental properties, and also does things like hiring people to repair her own house and planning trips. Bottom line, she is very busy and has trouble keeping organized. She expressed particular interest in keeping track of various deadlines, and also being able to record notes about various things she has to do, so that when she puts them on ice and comes back to them she has not totally lost her place. Other than that, I'm not sure exactly what she wants, but I don't think she wants a ton of fancy features--something moderate to simple is probably good.
I have been looking at various software, but it generally seems like most project management software is intended for project managers/teams. I am looking for software that would just be for her. Finally, it doesn't matter if it is web-based service or a desktop application, but I don't want to get her anything that you have to pay a subscription fee for. Either free or one time purchase is fine, just not a recurring fee (as those tend to add up).
I would definitely go with a web-based service so she has access anywhere and any device. Asana, Zoho, Smartsheet, Wrike, etc. - there are plenty. I'd just google search and review the public's favorite web-based options.