When Your Best Isn't Good Enough

I've realised that lately I've been a really crappy parent. And it hasn't just been for a little while, it's been for about five months, if not more. 
There are many reasons, but no excuses and frankly it's not good enough. Sure I've been tired, we've been moving, I've had a baby etc, but none of that is Chai's fault and he shouldn't suffer because of it. 
I used to be a fun mom. We used to do things all the time and get up to lots of adventures together. We'd go to the park, go for walks, find drains to drop things in, see the ducks, watch boats on the river, go to the library, go to rhyme time, stand on the side of the road and watch all the cars go past etc. Now we do nothing.
Admittedly I'm so exhausted that I struggle to keep my eyes open most days, but that's too bad. Chai shouldn't be bored and have to stay at home all the time just because I'm tired. We've been living here for eight months and I haven't joined a playgroup or found him any friends. He longs to be around other children. Whenever we come across other kids he gets so excited, it's not right that I'm denying him the opportunity to socialise like he so badly wants to.
I've talked about it with my mom and dad and they both say that he's a happy child and I'm doing the best I can. But that's not good enough. I need to do better. I want to be a great mum, not a mediocre mom.
With the school holidays coming up very soon most playgroups and other activities will be closed, so I need to find activities that we can do at home, things to keep him engaged and entertained. They need to be things that I can do with Eljay in my arms or in the wrap and some things that Chai and I can do together when Eljay is asleep. 
I'm going to get him a blackboard and some paints so we can paint together, what else can I get for him? 
I'm also planning on taking him to the park at least twice a week so that he can run around and play with other kids. 
So what do you do when your best isn't good enough? How do you keep your children amused all day? Does anyone have any suggestions for me?