I took a new credit card 2 weeks back and now I saw an exciting offer for a new travel credit card. I know there is definitely an impact because of the hard inquiry but would it impact the score in any other way? How would the credit unions treat this as? It sounds like I am going to more lenders all of a sudden and applying new credit cards.
Adding a card gives you a hard inquiry as you know. It also reduces your average account life, which is best when over 9 years. Both will impact your score a bit.
Last, while not really a function of the score, it becomes part of your available credit. This may seem obvious, but a bank that's about to lend you money, for a mortgage, for example, will look at the total credit you can tap, and take it into account, regardless if you are actually using the cards.
It will likely lower by a small amount. It's tough to know by how much without knowing more about you than you should post here. However, you can get a good feel for how much by searching online for "credit score estimator" and trying out a before/after calculation on your credit score.