Event Repeater can be a powerful tool if used properly. Below are some ways to make your repeatable events more immersive.

Using Event Conditions

By using the preconditions that are already a part of Stardew Valley, you can make events happen once a week, once a year, every day or when a specific thing happened before. A simple example is making an event only happen once a season:

   "79890001/u 28/sunny":

The preconditions on this event state that it will only trigger on a sunny day on the 28th of each season. This means that it will repeat only once a month if there is no rain or snow. There are many possibilities, try to experiment!

Using the Random Condition

You can make a Repeatable event more interesting by giving it varied versions of itself:

"50000000/d Tue Wed Thu Fri Sat Sun/z winter/r 0.5":
"50000000/d Tue Wed Thu Fri Sat Sun/z winter/r 0.3":

The two events above have the same EventID but the event themselves are different. One has a 50% of executing so long as it's a Monday that is not during the winter, while the other only has a 30% chance to execute. Once one executes.. the other is also labeled as seen. Event repeater will remove the ID the next day and when the conditions are right.. it will roll to see which event will happen.

Using Content Patcher Tokens to control Repeatables

Content Patcher adds more functionality than XNB modding will ever cover. Using it's token function, you can make it where some Repeatable events will stop repeating:

 {
   "LogName": "Dating Haley",
   "Action": "EditData",
   "Target": "Data/Events/Beach",
   "When": {
     "Relationship:Haley": "Dating",
    },
   "Entries": {
     "983980348/f Haley 2000/t 1800 2100": [Event goes here]
 },

The code above states that as long as you're dating Haley, the event will be preset and repeat. Once you are no longer meeting the requirements of this token, the event will disappear and no longer be there to repeat.
Be sure to read the Content Patcher Mod Author's Readme to get a better understanding of tokens.