The best thing to do at Alassio is just lay on the beach and enjoy the sun. When it gets too hot, take a dip in the Mediterranean to cool off. Take a walk along the edge of the water. If you've had your fill of the sun, there are streets full of shops to wander through, and enough bakeries, gelato shops and food stands to feed you for weeks.
If you are really feeling adventurous, join in with the Italian boys jumping off the pier. They will love it. Our friend Karen made quite an impression on them when she took the plunge. (The pier isn't too high - maybe about 12 feet off the water. I'd jump in if I were you, as I don't know how deep the water is and wouldn't want to dive and get seriously hurt.)
Quick Tips:
Bring a good beach towel for laying in the sun (something better than a little hotel towel). If you want a lounge chair and an umbrella, you will have to spend a little money to rent one - it was about for both for the whole day. You may be ale to rent towels as well, but I'm not sure.
Also, if you are just seeing Alassio as a day-trip, remember to bring a change of clothes, unless you want to make the ride back with your wet swimsuit bottoms soaking through your shorts. Also, be prepared to have sand everywhere on your body. You will have sand in places you didn't know you had, especially if you went in the water.
Best Way To Get Around:
There are trains to Alassio from most major train stations in the area - Turin, Genoa, Nice, about any train that runs along the coast will stop in Alassio.
Once you arrive in the town, just walk to where you want to go. It's a small town and everything is in walking distance. If you're staying in town and have a lot of luggage, you can catch a taxi outside the train station.