Yes, I had a cat who did this same thing!  Is your new cat a Siamese?  That
breed can often be very vocal.  My cat was a Persian, and she would
occasionally go to another room, or to another floor, and just meow.  I
would usually go get her and bring her into the room I was in.  I never
could figure it out - it seemed like she just wanted someone where *she*
wanted to be.

I have read that sometimes elderly cats can meow because they are confused,
or don't know where they are in the home.  It might be possible your new cat
is confused or lost in the house, not because of age but because of the new
location.  It's a good sign that she's eating and using the litterbox.  She
might just need a little extra reassurance while she is getting used to her
new home.

Meghan

It is natural.  It sounds like a wonderful cat.  Give it time to explore.
It may be just saying "look at this".

The cat I inherited from my brother did this a lot when I first got her. My
suspicion is as she becomes more comfortable that will diminish although she
sounds like she will be a "talker". I bet she has siamese in her lineage
somewhere. You might consider trying some Feliway to make her more at ease
(you spray it on furniture at nose level). Just give her lots of attention
and enjoy. Once she is confident you aren't going to "go away" I bet she
will settle down.

Karen

Have you got room for another cat? Maybe one she used to pal around
with at the shelter? If not, give her time and toys and maybe a cat
tree. Is there a window seat where she can look outside and watch the
birds, squirrels, and trees? Give her enough to occupy her and she
will adjust.

Bless you for adopting an adult cat from a shelter.

I wish there were more people just like you.

Turn on a radio so she will think someone is close by.  MLB