Is it worth doing a day hike of The Blue Trail in March? Weather wise? Are shops/restaurants open? Also, recommendations of where to stay as we do have a rental car and need to factor in parking and then hoping on the train.
Weather is iffy in March and nobody can forecast that far in advance. I'm sure there will be restaurants that are open. Monterosso is the largest town with most options, not only for restaurants and accommodations, but also for parking your car.
I'd suggest staying in Levanto. It's quite lovely and only a couple of minutes (by train) to Monterosso. We stayed there for a week this past May and it was perfect. Levanto is easier for parking for sure.
I can’t comment on CT in March, but years ago our tour stayed in Monterosso in September for a couple nights. That said, if we were to return, I would opt to stay in the less touristy Levanto. Our tour guides Aunt lived there. We went to a unique restaurant that had a stunning view of the valley and delicious cuisine. If you have a car it would be ideal. The restaurant is Zita. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj2k86N9uD8AhUNAjQIHcaCDvYQFnoECBcQAQ&url=https%3A%2F%2Fwww.zitalevanto.com%2Findex_eng.htm&usg=AOvVaw0Lwlgq1cOXEIQuo0XdtT5N