You are correct that you will not get many calls for jobs in Bangalore if you opt for Hyderabad as your current location on portals. In my experience, you can certainly mark your location as Bangalore. Once you get a call, you must explain the genuine reason for shifting your base location and tell them that you can attend an interview in Bangalore on 24 hours' notice. You can also get a new SIM card for Bangalore and mention the same on your CV, as most consultants will hesitate to make a standard call to candidates. I think it would work. Furthermore, it's not about lying but making job portals work for you technically in changed circumstances, as all the information on your CV is genuine except the location.
Regards,
Vikas