How should a recent graduate handle salary negotiations?

As a recent graduate, I’ve received some calls regarding job opportunities at a service-based company. After my interview, they expressed interest in moving forward with my application. When discussing my expected salary, I provided an average figure based on what my peers from the same department typically receive during campus placements. However, the HR informed me that this amount exceeds their budget, and they offered me a very limited salary range.

The dilemma is that the client company I would be working with is quite reputable and has a strong industry presence, but it would require me to relocate to a location I’m not particularly fond of. I communicated my hesitation about moving, and the HR suggested that I could potentially switch locations after some time if my manager approves, which I find hard to believe. I’m open to relocating if I receive a higher salary, but considering the current job market, I’m worried that insisting on my expected compensation might jeopardize the opportunity.

So, should I negotiate further? If yes, how can I approach this without any prior experience? Or should I simply accept their offer at the higher end of their budget?