April’s possibly too early for big climbs, because the high mountains will still have snow on them and/or the weather could be iffy.
My recommendations:
1. Lake Como
Stayed in/near Bellagio – did a lap of the lake (100 miles), rode Madonna di Ghisallo climb (a classic), the Sormano (ridiculously steep), rode to Lake Lugano and back, plus lots and lots of BIG climbs on both sides of the lake.
2. Bormio, Italy
The Stelvio of course (from both sides), plus the Gavia, Mortirolo etc…
3. Pyrenees
Just got back from riding Tourmalet (both sides), Col d’Aubisque, Hautacam, etc in the Pyrenees – also great but April too early for these, plus…
4. St Jean de Maurienne – has 5 out of 10 of the TdF’s top climbs in the vicinity: Col du Galibier/Col de Telegraphe, Col de la Croix de Fer/Glandon, Col de la Madeleine, Col d’Iseran, plus Alpe d’Huez is not too far away in Bourg d’Oisans