Was there in May a couple of years ago and it was greyish and wet - but that's weather for you -it varies!
Good place to go though- we were in the marina in centre of the city quay - can't remember the name. V smelly - there is raw sewage pumped in directly, you get used to it after a while.
For food - ignore tourist trap places on the piers, cross the main drag that runs along harbour front and get into the labyrinth of narrow streets of the old city - losts of very good, but reasonable priced restaurants.- as long as you like Italian food of course, coz like everywhere in Italy - that's pretty much all you'll get.
takea ride up the Biggo - a kind of glass bubble lift - for great views of the city and get your bearings for walks around the re vamped dockland area.
if you have time to spare, definitely worth visiting Cinque Terra, accessible via rail from Genoa it's something completely different, well worth it! Was there (driving though) a month ago, amazing place
last summer we cruised along the coast from Rome to France,
the ligurian coast from La Spezia till Portofino ,
oa Cinque Terra was the best part, and really worth a visit,
even better by boat
Hard to say about weather, we usually go at the other end of the season for the boat show in October and we've had everything from blazing sunshine to serious storms.
The old town is a great start, a very quaint tangle of old cobbled streets with bars and restaurants all over the place. Two recommendations for food would be Il Guscio on Via Ottobre and L'aragosta in the old town.