The QDR is a safe place to deposit qualitative data. It has been certified as a "trustworthy data repository" by CoreTrustSeal. In tandem with the researchers who deposit data with QDR, its trained staff fully curates data to make them usable, discoverable, meaningful, citable, secure and durably preserved. NYU is a member institution of the QDR and so you can deposit your own qualitative data there, as well as use the data of others!
To register for an account with the QDR:
The UK Data Service is a a place to both deposit data and find secondary datasets for use in your analysis.