What some alternative ways to present tabular data instead of the standard table in the UI? I don't want the data to be displayed in formal tables with rows and columns. Is there any way of grouping them all and show it attractive and nice?
If the data is tabular, then I see no reason why one shouldn't go with tables? After all, the whole purpose of table element is for showing such type of data.
But if your query is how to make the tabular data look more beautiful, then read this article - http://darkhorseanalytics.com/blog/clear-off-the-table/
In nutshell, it follows the principle of 'Less is more' by removing colors, removing grid lines, aligning items based their types (Numbers or String) etc.
Also another method would be to use graphical elements like Pie Charts, graph bars etc.
Note: Tables are not old-fashioned. But using tables for layout of elements is.
Have you considered using cards to display your data? They're becoming very common with Google's Material Design and can be quite appealing to the eye if styled correctly.
Ofcourse placing too much detail in a Card is "against the rules" but it is a viable alternative.
For convenience, you can always provide a button which changes the view to display the data in a table.
Another useful article which backs up what most of the others have mentioned before but in a little more detail is this: https://design-nation.icons8.com/intro-to-data-tables-design-349f55861803
It provides you with a wider variety of examples for specific cases.