I grew up 4 miles from the Delaware border, in Pennsylvania.
No idea about income or property taxes. However, there is no sales tax. Taxes on other stuff like gas and booze are low, compared to neighboring states.
Yes, there are beaches. Dewey and Rehoboth. One is more known for the "alternative lifestyle" crowd.
The other is pretty good, regardless. Used to spend some time at the Rusty Rudder bar down in Dewey when I was younger. The Delaware shores are plagued by the fact that they are near a lot of outlet malls. The traffic is horrendous, but then again you can say the same thing about the NJ beaches.
The University of Delaware is a good school. Not top tier, but a good solid state school. There's also Delaware State University.
I would not want to live within the city limits of Wilmington. There is some nightlife/culture, but Philly is better and it's only 30 mins away. Not sure about Newark, which is mostly a college town with the University.
Delaware is not shall-issue (like PA). However, despite the rather long list of things you have to do to apply for a CCW, it is basically shall issue in that if you jump through all the hoops (safety class, etc.) then you'll get a permit. No Class 3. Instant check on all guns, no waiting period.