What's the best neighborhood in Oakland for a first time visitor?

We'll have to see what others say, but I suggest Jack London Square.  The Waterfront Hotel and the The Inn at Jack London Square are both really nice. There's lots to do around Jack London and you can use it as a base to walk (or bike, or drive) up into Oakland.  It's not too far to Old Oakland around 7th and 8th Streets.  And then you can just keep going up deeper into the city from there.  

I live in Oakland, but am not very familiar with hotel options. If it were me, I'd want to choose a little B&B or something in the Rockridge neighborhood.College Ave. is a wonderful street for shopping and the subway station (called BART) is there as well. I also like the Piedmont Avenue area, although a BART station isn't walking distance.The downtown area has a gorgeous natural "lake" called Lake Merritt (it's actually a tidal estuary, but it looks like a lake and is referred to as such) and probably has the best choice of traditional hotels. If you're around on the first Friday of the month then you might enjoy walking around the downtown area's funky art & food scene then.

So look for places to stay which are in those interesting areas. And have fun! Oakland is such a beautiful city.