Narva is small and the centre is walkable, so the real question is whether you sleep by the castle, thirteen kilometres north at the beach in Narva-Jõesuu, or not at all.
The centre — Peetri plats and Puškini
Between the castle, the town hall square and the station, all within ten minutes of each other, with most of the hotels and restaurants in between. Functional rather than pretty — the old town was destroyed in 1944 — but it puts you next to everything.
Narva-Jõesuu — the beach
Thirteen kilometres north, where the river meets the sea: sand, pine dunes and spa hotels with pools and saunas. The right choice in summer or if you want the spa. Out of season it is very quiet, and you are dependent on the bus or a car.
Joaoru and the riverside
The strip along the Narva river below the castle, with the promenade, the recreation area and the beach house looking straight across at Ivangorod. Guesthouses and apartments rather than hotels. Good for the view, less good if you dislike walking uphill into town.
Practical: it works as a day trip
Most people see Narva in a day from Tallinn. If you do stay, note that the city runs 13 bus routes at roughly two an hour between 6:00 and 23:00, so evening moves and the trip out to Narva-Jõesuu both need checking against the timetable.