Ferries arrive in Capri from the mainland at the Marina Grande. Regular buses run to Capri town from the Marina.
There is also a funicular railway running regularly and railway porters will deliver suitcases to Hotel La Reginella for a fee which, if you are carrying heavy bags might be worth considering, given you are already making savings by sensibly choosing to book a economical room in budget accommodation whilst in Capri.
To reach La Reginella di Capri hotel, the easiest way is:
From Piazza Umberto I, turn left and head along Via Longano, then you will reach Via Sopramonte, go through this street up to Via Matermania, at 36 you will find La Reginella Hotel Capri.
On Google maps click on http://g.co/maps/dsxmx
The 2 star Hotel La Reginella is situated on the cliff top overlooking Capri. This is a no traffic zone but is an easy walk from the Piazzetta.