In reply to Bonna:
All three are good, but Nice has the closest climbing to the airport - you can even see St Jeannet from the runway.
Much depends on whether you intend to hire a car
Barca - 90 mins to Costa Durada, less to Monserrat
Nice - 30 mins to La Turbie or Peillion, 20 to St Jeannet and about 10 to Colle sur Loup
Genoa - 60 mins to Finale (which is only about 90 from Nice)
Public Transport - Genoa, bus to the station, train to Finale, bus to the crags
Other options Verona and Brescia are handy for Arco and Garda area