We present hybrid-integrated extended cavity diode lasers tunable around 637 nm, with a gain-wide spectral coverage of 8 nm. This tuning range addresses the zero-phonon line of nitrogen-vacancy centers and includes the wavelength of HeNe lasers (633 nm). Best performance shows wide mode-hop free tuning up to 97 GHz and a narrow intrinsic linewidth down to 10 kHz. Also, the maximum output power is 2.5 mW in a single-mode fiber, corresponding to an on-chip power of 4.0 mW. Full integration and packaging in standard housing with fiber pigtails provide high intrinsic stability and enable integration into complex optical systems.