Yes, 3 nights at Kila for your beach experience!

Ubud will give you a very good taste of Balinese culture along with awesome rice paddy and mountain scenery. Definitely recommend. Certain parts of it might be slightly touristy but if you do the activities proposed by a hotel like Amandari you will stay true to the culture and off of the normal tourist path.

Jiwo would make an awesome addition to the above as you will find the culture different (muslim, not hindu, etc.) and you will enjoy the volcanoes and ruins.

Check with Aman on their packages combining the above properties. There is usually lots of value in extended stays and combining properties.