Yes — Birmingham is generally safe for tourists, and millions of visitors enjoy the city every year without incident. The city centre, Brindleyplace, the Jewellery Quarter, Digbeth, and Bournville are all well-policed and comfortable to explore day and night.
As with any major European city, normal urban precautions apply: keep bags secure on public transport, be aware of your surroundings in busy nightlife areas late at night, and avoid leaving valuables visible in parked cars. Areas around some suburban ring roads and parts of inner-city neighbourhoods away from tourist routes are best navigated with local knowledge — your hotel can advise.
Emergency services are excellent. Dial 999 for police, ambulance, or fire. NHS urgent care walk-in centres are available in the city centre for non-emergency medical needs. Birmingham has a large, well-signed transport network and well-lit main streets, making navigation after dark straightforward for visitors sticking to main routes.