In Asia, in particular Thailand and India, there are a lot of cheap and popular dual SIM phones. In fact most people seem to have dual SIM phones - I'm not particularly sure why, but I think multiple boyfriends/girlfriends may be partly the reason.
These are all quite similar to the good old Nokia 3310, that is to say, a physical keyboard, and a small, non-touch, screen. These are often around the $40 mark or less, so well within your price bracket. The Nokia 107, for example:
Some others are the Nokia 206, 208, 215, 220, 222, 225, 301, and 515.
This is by no means the full list, but as you can see there are plenty to choose from. Whether these models are available in your country is another question, as they are obviously targeted towards the emerging nascent mobile phone markets, where lost cost is important. In more affluent countries, these may be considered "throw-away" phones, but they do meet your criteria, and do make for great holiday phones.
Also, because there is no touch screen and a smaller screen, the battery life is longer on these phones in general, and only require a charge every other day, unlike most smart phones.