Susan,
IMO, Monterosso would be the best choice as it's relatively flat for the most part. It's an easy walk from the "new town" to the "old town" and a few stairs from street level to the train platforms, but you can take those at your own speed. I'd suggest at least a two night stay in the Cinque Terre, which will only provide about a day and half for touring. Three nights would be better (depending on the weather).
There is a car park on the beach in the new town and another in the old town (I can't remember what the rates are?). As I recall, the two parts of Monterosso are accessed by different roads. You won't be able to drive between the two parts of town due to a ZTL zone (hefty fines!).
The previously mentioned Hotel Pasquale would be a good choice, although if you stay there you might want to park in the old town. That might not be the best idea in your situation as the road from the hotel to the car park is uphill so it might be a challenge for your mother. You could also consider Albergo La Spiaggia in the new town, which is relatively close to the car park on the beach. I've never stayed there but have heard good reports about it.
Another good hotel possibility is Hotel Villa Adriana which is at the far end of the new town along the road into Monterosso. They offer free parking so that's something to consider. The hotel is a bit older but it's clean and comfortable, has an Elevator and as I recall they serve a nice breakfast. It's a bit of a longer walk to get into the main part of town, but it's relatively flat so it's not difficult.
There are lots of nice restaurants in the new town and many more in the old town within easy walking distance. Cantina di Miky is a big favourite with many here (if the weather is nice, sit at their outdoor patio overlooking the beach). The more upscale (expensive) Miky restaurant (owned by the same family) is at the far end of the new town, closer to Hotel Villa Adriana. Be sure to try something with Pesto, in the area where it was invented.
One caveat about hotels in Monterosso (or anywhere in the C.T.) is that some may not be open in March. As your dates are flexible, you might want to schedule your visit towards the end of the month. You can always check with the hotel.
As mentioned previously, the Ferries probably won't be operating that early in the year. When they are operating, the ferry dock is in the old town area, and there's a ticket booth right there. It's very easy to get between the five towns using the frequent local trains. As you're probably aware, if you're buying tickets locally for Regionale trains, these must be validated before boarding the train on the day of travel, although the rides between the towns are only 5-10 minutes each so your tickets may not be checked. Monterosso has a "full service" rail station and the agents speak English (to some extent).
There will be a few steps to deal with when visiting the towns.....
- Riomaggiore: steps to use the sottopassagio (transfer tunnel), depending on which track you arrive / leave on.
- Manarola: relatively flat although the main street becomes steeper the further up you go.
- Corniglia: the town is high on a bluff and takes 300+ steps to get there from the station - there's a shuttle from the rail station to the town (small extra charge unless you have a Cinque Terre Treno card).
- Vernazza: steps from the station down to the main street.
I'm assuming that as you'll have a car, you'll be using the compulsory *International Driver's Permit".
Buon Viaggio!
