I've lived and worked in Downtown Long Beach for about 3 years now. Like with anything, there are pros and cons. Overall, I really enjoy the city. I'm walking distance to good restaurants, theaters, the marina - and I never feel unsafe to take advantage of that. It's convenient to hop the Passport to Belmont Shore, or even the Blue Line to Downtown LA. If you're out in the community enough, it's not long before you get to know the local business owners and familiar faces around town. It's feels small and friendly.
Downtown is mostly condo/loft living. Make sure to research the HOA before committing to any property. Some of the older buildings can also have pest or plumbing issues if they're not properly managed. I'd make sure to purchase a unit that includes parking or else you'll end up renting a spot for at least $65/mth (and not necessarily close to home). Guest parking is usually challenging, but not impossible. Also, living Downtown puts you right in the middle of community events, festivals, and the occasional movie production - which can be both convenient and inconvenient.
Good luck with your house hunt! DOMA Properties is a great resource for questions about real estate. We're located right on Pine & 4th Street in the heart of Downtown.