Answering your questions:
Valencia is smaller than Barcelona or Madrid and cannot be compared to these cities. Its population is about 800.000 people or maybe a little more.
It's not as cosmopolitan as Barcelona neither as full of places to visit as Madrid. It hasn't many restaurants or theaters. Despite the traffic is horrible and parking is difficult (even being not a great capitol), it is a more calm city than Madrid or Barcelona, usually has sunny weather -the winter is not very cold- and it can be a nice city to walk through or to go to the beach. Not as beautiful as castillian or northern cities, but taking a walk won't be unpleasant. Especially through the "river", that is, the former Turia river's bed, which was dried some years ago and fullfilled with a park of some kilometers long (this park is usually called "el río", The River)which ends at the Oceanogràfic aquarium.
The city is not very popular among tourists, except during the "Fallas" celebration (march 14-19th). You know, when they build those colored wood and paper sculptures all over the cities (about 400 "fallas" are built, and about 300 little infantile "fallas"), and then burn the sculptures on march 29th (St. Joseph). In those days, the city is full of people -specially the town center-, many streets are closed to traffic, and many people throws firecrackers. Don't miss the "Fallas" celebration, I guess you'll enjoy it.
Of course, the meal to eat is the paella. Tourist use to prefer the seafood paella, but ideally the best thing is to find someone who cook a real traditional valencian paella, with chicken, and, if you like it, rabbit and, rarely but advisable, duck.
I don't think that Valencia represent exactly the idea that a tourist have about a "typical spanish city" (for example Toledo, Cádiz, Segovia, etc...) , and it's not a cosmopolitan city with many touristic places like Madrid or Barcelona, and is not a small pretty city sorrounded by beautiful landscapes as some cities in northern Spain. But it's a sunny city with an easy walkthrough. There are some places to see, maybe not the usual touristic spots, but you could, for example, take a small boat trip through the Albufera or visit some not well-known old buildings and small art museums.
Don't miss the "Oceanogràfic", actually the largest aquarium in Europe.
Some "Río" park views. The "Music Palace".
The "Hemisfèric" (Imax teather) and "Science Museum" buildings.
Some city views The "Quart Towers", an ancient city wall remaining entrance (the wall was destroyed).
The "Serrano Towers", another city wall entrance.
The "Micalet" or "Miguelete" ("Little Michael") tower, from 1400.
The train station, at the left, almost out from the picture, the "Plaza de Toros" (bullring)
"Plaza de la Virgen" (virgin square)