Where is jurisdiction proper?

D is required to register here in Galveston county, his residence is Galveston county. He failed to report more than 48 hours in Nueces County, and did not report in person to Corpus Christi PD in new county of residence not later than 7th day.

So, which county has proper jurisdiction? The county where he lives and reports which is Galveston county, or the county where he didn't report after staying longer than 48 hours and the 7 days?

I think you are actually talking about venue and not jurisdiction. The following is from Rodriguez v. State, 2014 WL 1395455:

The Texas Code of Criminal Procedure specifically provides for venue in a prosecution for the failure to comply with sex offender registration requirements:
An offense under Chapter 62 may be prosecuted in:
(1) any county in which an element of the offense occurs;
(2) the county in which the person subject to Chapter 62 last registered, verified registration, or otherwise complied with a requirement of Chapter 62;
(3) the county in which the person required to register under Chapter 62 has indicated that the person intends to reside, regardless of whether the person establishes or attempts to establish residency in that county;
(4) any county in which the person required to register under Chapter 62 is placed under custodial arrest for an offense subsequent to the person's most recent reportable conviction or adjudication under Chapter 62; or
(5) the county in which the person required to register under Chapter 62 resides or is found by a peace officer, regardless of how long the person has been in the county or intends to stay in the county.
TEX.CODE CRIM. PROC. ANN. art. 13.31 (West Supp.2013)


Hope that helps.

Got it, thanks