If you want to go back for about 3000 years - Sardinia is a good place to start. There are still over 7000 of mysterious structures left by Nuraghi civilization. Sardinia also boasts of the first Phoenicians city Nora founded in the 8th century BC. You can get there from Cagliary passing through busy town of Pula. Entrance fee is just 5 euro but guided tours only (in English also). Place is absolutely fantastic and in this case information given by the Italian guide was surprisingly interesting (I am not really fond of guided tours!). Basically you can see everything: central piazza, baths, shops, houses, rooms and even toilets (we were told that Phoenicians used to chat while doing their "business"!)
Back to Cagliary - capital of Sardinia. It sits on top of a hill overlooking its beautiful bay - the Bay of Angels. The best view is from Bastione Saint Remy. The most exciting way to see Cagliary's old city is probably by the Segway scooters. One tour costs 25 euro and lasts for about 1h 30 min, just check on www.newwaysardinia.it
8 km southeast of Cagliary lies Poetto beach (6 km stretch of soft, white sand) - much liked by locals and visitors alike. Not far from it in Quartu Sant Elena you can watch wild flamingos (very pink!). From Cagliary you can take a train across the whole island to Sassari (it costs just 15 euro and takes 3,5 hours). It's the same by bus but costs a little more - 20 euro. Scenery is absolutely stunning: green valleys, steep hills, Nuraghi ruins, mountains with white (snow) caps. It looks so peaceful and idyllic that we felt surreal when at one station local polizia caught a stowaway and literally dragged her to the nearest police station. What a contrast!
Sassari is Sardinia's second city - old town full of crumbling houses, streets are very narrow and washed clothes (even bras!) hanging out of windows practically everywhere! The Chiesa di Santa Maria di Betlem (1106) is lovely as is Duomo di San Nicola. The Teatro Civico is now open (after restoration) and as a miniature version of Milan's La Scala opera house is worth a visit.
From Sassari in just 40 min you will get either to Fertilia airport (notably for Ryanair flights) or Alghero - town with distinct Catalan character. The shops here are full of coral jewelry and carvings. My wife bought a sea urchin (his spikes were still very sharp indeed!) and sent it home by post. Surprisingly it arrived safe and sound one day ahead of us!
Just 24 km west of Alghero is spectacular Capo Caccia and its famous Grotto di Nettuno (guided tours only). But before you see these fascinating caves you have to undertake the vertiginous 654-step descent down there. The Italian army base is actually next to it. From Alghero go to Bosa - charming little town founded by Carthaginians. Be careful if you take local Fds bus, it goes along the coast, up and down hills, view is just fantastic but it drives so fast you get a feeling like participating in Formula One race!
If you fancy good Neapolitan pizza I would suggest a trattoria "Rossopomodoro" - excellent service and mouthwatering pizza (prices are very modest and menu is in English). You will find it on the corner of via Sassari and via Crispi (just off piazza Matteotti in Cagliary). Trattoria "La Pirata" is very good for Sardegna specialities like burrida (kind of fish stew) or some grilled fish like Spada alla Sardegna (swordfish steak) (viale Regina Margherita, Cagliary). Pecornia is Sardinia's best cheese - it's hard cheese and pretty fatty but very tasty! Myrtle liqueur (30°) - obtained from wild myrtle berries or leaves tastes like some cough mixture but it's Sardinia's national drink!
In Alghero I would recommend to stay at Hotel Alguer, it's just 10 min walk to the town center and 5 min to the beaches. Rooms are spotless, BBC  channel is available and guys at reception desk are very friendly and nice to talk to (they speak fluent English too!).
Overall I could say that Sardinia is the place where you definitely want to come back.
The bedroom of a wealthy man
In Cagliary
Nice doggy!
Some plant at Capo Caccia
The cathedral in Sassari
Typical narrow street in Sassari
Nora - the first Phoenician city (8th century BC)
The wall of old town in Cagliary
Burned down boat in Bosa
Everlasting Date palm tree in Alghero
Sad Jesus in Alghero
"Beauty" of Sassari's main street