Applying for jobs in a new city before having a local address

I'm applying for jobs in a city I intend to move to, but the move depends partly on finding work. Applications often ask for a local address, and I worry my current location makes recruiters assume relocation will be difficult. I can cover the move myself and be available for interviews remotely. Is it better to state ‘relocating to [city]’ with an honest timeframe on the resume, or explain the situation only when contacted?