Yes, but the mobile network is often better and more secure.
WiFi is available in many hotels and restaurants, but the quality is not always that good.
The 3G and 4G network in Indonesia, on the other hand, is pretty good and often faster (and more secure) than the average WiFi connection.
If you have a simlock-free telephone, it is advisable to use an Indonesian prepaid SIM card in your telephone. In Indonesia you can buy a SIM card with a data bundle quite cheaply. Make sure you buy an Indonesian SIM card on arrival at the airport. Here they can unblock your phone and make it suitable for the Indonesian network. It is difficult to find other places in Indonesia where they can help you with this.
This way you can continue to use the internet cheaply and quickly as you are used to.