Been twice in the last 5 years to Alghero, Late May and early September - both times weather was variable - so April could be risky, but you may hit a heatwave. I think the peak season is July & August, so you'll find outside these times it's reasonably quiet.
The west coast is a bit like the west of ireland in parts, very natural. I have a friend who went to the south/south west and thought the beaches were like the carribean.
For a week, Alghero is a good base, alternatively you could hire a car from Alghero airport and meander around - the roads are very quiet.