Optimal way to create a feature set? I have a time series data (say weather data for each day for one week) that changes at each time step. Along with this, I have some data that is fixed (eg - the latitude and longitude of this place where weather measurements were taken). Is it wise to repeat this fixed data at each time point to train my LSTM family model?

If this fixed data can be similar or even partially equal for different time series and you expect the fixed data to contain information that is relevant for your time series analysis task (prediction?), this data should be included, and one way is indeed your method to add it to each time point.
Another approach could be to initialize the LSTM state with this fixed data. There are many other possibilities, e.g. having the LSTM state being learned from the fixed data. But I think yours is the most straightforward. However, you would need to check out which variant works best for you.
