Is there any way to find out which nursing home my aunt was admitted to?

If you know what hospital she was in, call that hospital and the floor she was on and ask to speak to the discharge planner. I'm not promising they'll tell you anything but the discharge planner is the person who takes care of all the discharge paperwork, transportation and anything concerning her discharge from that hospital. Good luck!

Maybe her neighbors know, maybe one visited while in the hospital.

Yes, what is your source of information to date? How long has she been gone and you don't know where she is? Is someone shielding her from you for a reason?

As above, create a way to get the information you want. You might want to use two different phones or enlist someone for additional help.
Also, if you say that you tried to send flowers and the florist called you saying they were denied delivery ,you might be able to get an answer from the hospital. If you are really concerned go ahead and send flowers..with the understanding the you want to know they are delivered to her, with signature from her. Ridiculous what we have to go through, but I understand why.

Call the hospital switchboard, ask which room to send flowers to your aunt.
When they tell you she has been discharged, ask if you could send flowers to the Nursing Home.
Then, ask to speak to the discharge nurse, or the nursing station she was at.
Say you sent flowers, will they be forwarded for you?
This maybe won't work, but is a good test of HIPPA laws.

Haileyalar, where was your Aunt living prior to be taken to the hospital? And who called for the ambulance? Someone has to be her caregiver, or Power of Attorney, unless she is a ward of the State.

Does your aunt have children, and if so, are they involved in her life? If so, they should know where she's been taken.

You can call nursing homes and asked to be connected to "Mrs. (your aunt's name). I've done this when searching for a relative in a hospital and it worked.

I'm not sure if they would tell you due to privacy laws, but you could try asking the hospital social worker or the local patient transfer companies.

How did you find out she was even in the hospital?

Call her local police non emergency and ask them..