Hellobee Boards

https://www.amazon.com/gp/aw/d/B076QDMKSW/ref=mp_s_a_1_15?ie=UTF8&qid=1526300393&sr=8-15&pi=AC_SX236_SY340_QL65&keywords=3T+swim+cover+up+girls Nautical Tassel Swimsuit Coverup...there’s so many to choose, but this one seemed a little Country Club-ish to me.

A fun towel! Costco had Mickey and Minnie hooded towles a few weeks ago. I'm sure Amazon has something similar. Mermaid theme would be cute too.

These were all the rage with my girls and their friends (3 & 5 last summer) last season at the pool:

https://www.amazon.com/Barbie-Dreamtopia-Rainbow-Lights-Mermaid/dp/B015CCR1FW/ref=sr_1_1_sspa?ie=UTF8&qid=1526304239&sr=8-1-spons&keywords=mermaid+barbie&psc=1

There are also non-lighted versions which are a little cheaper.

Also, these (if the girl is a decent swimmer/gets her face wet):
https://www.amazon.com/SwimWays-Disney-Princess-Ariel-Glitter/dp/B01MTNIOLS/ref=sr_1_2?s=toys-and-games&ie=UTF8&qid=1526304332&sr=1-2&keywords=ariel+diving+toy

Otherwise, cute sunglasses and a cute/kind of outrageous straw or sun hat? She can wear it to the pool or for playing dress-up, whatever she decides.

FWIW, we go to a "country club type pool", and all of these toys would be fine. But you're correct that floats are a no-go.

I like board games that the family can play together, Amazon has a ton and the suggestions are often things that I would never have thought of.

I like the brand Blue Orange in particular.

Our 3 year old son's big thing this year has been "tiny sh*t" - little trinkets and treasures he finds important. He also finds sunglasses to be vital. All this has led to him needing a man purse or bag or many, many pockets. At this point, he has like 2 purses and I'm looking into a small fanny pack for him. So especially for a girl, I'd look into a bag of some kind filled with summer essentials like sunglasses and/or a pretty water bottle.

we picked my son's favorite book at the time ("The Book With No Pictures") and i bought 20 copies all at once time on Amazon. EVERYONE we know got it for their 3rd birthday, boys and girls. It couldn't have been simpler!

For summer birthdays, if I wasn't giving the book, I would gift a giant box of chalk or a big tub of bubbles - something simple that they can enjoy outside.

Below are a few things both my girls - almost 3 and 5 years old enjoy:
1. Kwik Stix: https://www.amazon.com/Pencil-Grip-Tempera-Drying-TPG-602/dp/B013HO4OR0/ref=sr_1_3?ie=UTF8&qid=1526348733&sr=8-3&keywords=kwik+stix+tempera+paint+sticks
2. Boogie board. My kids love theirs.
3. Puzzles! I'm a fan of the mudpuppy brand as well as crocodile creek
4. Costumes for dress up