I sympathise, as I still find it a bit weird when my children go to see their dad for the weekend - its only once every 6 weeks for us, but even so it is such a change from our daily routine, that I feel lost without them. I've been a single parent for 4 years now.
When the children are away, I always make at least one plan in advance - I have one single friend, who I will plan to see, but if not I'll make plans to pop over to my sisters house for dinner, or to see friends who are in couples, at their own houses. I think the husbands find it a bit weird to start with as they don't have a male to chat to, but they get used to it. I change who I see all the time so it's not too much pressure on them though.
I also book an exercise class and pay in advance - I am not a member of a gym but there are a few local classes that can be booked online. This gets me out for a bit and really clears my mind. It is nice to go to the same classes each time and build up some small friendships there as well.
Then I will usually also book a haircut, I take a book to the hairdressers and read uninterrupted for ages, and I also chat to the hairdresser as she is lovely.
Other things - I get the food shop done and make sure house is tidy so I am not running around again when they are back home.
I make a list of small jobs during the week, and leave the list to do when the children are away - this week I had to drop a bag to the charity shop, and take some stuff to the local dump. My car headlight has stopped working, so I also went to buy a new one, and then worked out how to fit it in myself (youtube!).
I find the evenings quite lonely, so if I am not going out I usually watch a film till late and then I am ready for bed, or read my book in bed.
I also catch up on sleep.
I can't say its perfect or that I really enjoy it, but a lot of it is just about keeping yourself busy so time passes.