I am moving to a different state, can I file bankruptcy there or do I have to file elsewhere?

Typically you have to live in the BK district for last 3 months before being able to submit to its jurisdiction.

Basically, you can file in the state of which you are a resident.  However, certain property is "exempt" (cannot be taken) when a bankruptcy is filed.  Under federal law there is a list of such exemptions; some states additionally have their own list of exemptions and the debtor can decide which list they wish to use. 

In order to use a state's exemptions, however, you must have lived in the state for 2 years.  If you have lived there for less than 2 years, you count back 2 years from the date you file for bankruptcy and then look at where you lived for the 180 days (6 months) before that.  Whichever state you have lived in for the longest time during that 6-month period is the state whose exemptions you can use. 

Note:  Some states, though, don’t allow you to use their exemptions unless you currently live in that state.  If you get caught in this gap, you’ll have to use the federal exemptions.