My secret weapon for the past 4 months or so has been the Treasure Basket. It's basically just a basket filled with things that are safe for E to explore with supervision. I tend to bring it out on those afternoons that are particularly rough, where he's just not happy doing anything. The appeal of the Treasure Basket, I think, is that it's not seen every day (or even every week), and sometimes it has new things in it.
I introduced the Treasure Basket at around 6 months. It was perfect, because E was new to sitting up unassisted and I was trying to encourage him to do so as much as possible, something he was way more likely to do if he was focused on holding something in his hands (otherwise he just wanted to roll around on the floor). [A short video of E exploring his Treasure Basket at 6 months.]
Since then the contents of the basket have changed slightly, as I add items and take away others (for instance, he used to have a jar lid, which he liked, but then he started scraping the paint on the lid off with his teeth, so that went bye-bye). Currently, his basket includes: a spiky ball, a wooden block, a plastic measuring cup, a loofah, a teething bracelet, a plastic egg, pieces of ribbon and ric-rac, a small jar of dried beans, and a wooden sock darner.
Assembling a Treasure Basket is fun because almost anything can go in it, including things you wouldn't want baby playing with unsupervised (like the jar of dried beans). It's a good opportunity to explore different textures and sounds. Don't forget to get the extended family involved in curating items; my mom looked around her classroom and contributed the blue ball, plasitc egg and little felt dog (no longer in the basket because I was concerned about his button eyes coming off in E's mouth). For the actual basket, I used one I had picked up at Target right before E was born, but I think a child-size Bolga basket would make the best Treasure Basket.
If you're the overachieving type you can create a Treasure Basket around a theme, like a particular color, or items that make noise, or are made of metal, etc. I've not done this yet but it's something I'll consider for when we start doing slightly more structured activities after his first birthday.
Once you present the Treasure Basket to baby you can take the opportunity to explore each item together, naming it and talking about the item's qualities (i.e., "Look at this blue ball! It's spiky!"). Older babies will need less help taking the items out and will more interested in exploring independently. E is at this stage now, so I usually just sit back and watch how he interacts with each item and what captures his interest.
I started a Pinterest board with Treasure Basket ideas; worth checking out if you're wondering what you already have around the house that would make good "treasure" for your babe. (And if you have a "secret weapon" toy or activity, please share in the comments!)