This really depends on your business or organisation, and what you think your customers or members are likely to be doing at the time.
It's always best to benchmark yourself by running tests at different days and times....you can even run tests at the same time but use slightly different words in your text message to see which one pulls a better response.
So is Monday better to send than a Friday, for example?
Maybe... maybe not.
Let's say you're a food retailer with weekly specials. It might be good idea to stick to the same time every week, so people come to expect it. Perhaps a Monday at 10am so shopping lists can be added to.
But you probably wouldn't do this if you're a clothing or other type of retailer, as this may annoy your customers. I'd recommend sending out "alerts" when you have new stock in, so your customers feel like they have the VIP treatment. These types of "alert text messages" really can be sent at anytime, but say you want to drive some traffic into your store during the week...perhaps send it on a Tuesday, and say "get in ASAP before it sells out".
OR maybe a Friday afternoon or Saturday morning when they are in more of a leisure mode.
...and don't forget to monitor any replies as people will likely ask questions or may ask you to hold onto something for you! (You can do this via your Account settings...call 1300 668 287 or email us if you need help on this.).
For nightclubs and restaurants, what about a Tuesday around 4pm (a typically quiet night for many eateries). "come in tonight for 2 for 1" or "free dessert" or "chef has top quality fresh salmon in tonight only".
Or a café that caters for workers....a text message at 11am when one's mind is usually on the luncheon meal! "Hot roast beef rolls with gravy today! Get em while they're hot. text back to order yours now."
Say if you're a club organising an event? Maybe a month ahead, plus follow up reminders would do the trick. I think any day would be fine for this...
There is also nothing wrong with mixing it up to see what day works better for you. SMS messages sent to customers can be easy to track in regards to responses, and if you need some ideas, we're always here to help.