Hey sweetie,
Hugs
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They can be tricky at this age even when they are fairly independent playing because they really don't play "games" yet, so you are kind of making up the play.....
Umm, trying to remember what DS liked at this age....books books and more books, playing in water, he also loved (LOVED AND STILL DOES) his little plastic yellow, blue and red bike....you can still get them. He was a bit older but just walking independently when he first started using it, so she may be ready....hours and hours of entertainment for him, his sister (who is 7yo and still manages to get around on it)...and I'm sure his little sister if she is allowed and when she is ready!!
To be honest if she is going through a really clingy stage, rather than trying to get her to play independently I would just try and include her in what you are doing....so if you are cooking and cutting up veggies, get her in her high chair "helping"...give her some grated carrot, some potatos to feel and touch etc. If you are cleaning, give her her own little bucket and cloth (and some water if you dare) and get her to "help" you...
I tend to do this as I'm not great with "activities" but I've noticed the kids LOVE doing what you are doing at this age...
gtg but I'll be back later if I think of something more helpful
xxL