Below I list some websites that I visit very often. They are not very neatly categorized. I may do so at some point in time.
IIIT Manipur
Cardiff University
University of Vienna
Tezpur University
The Abdus Salam International Centre for Theoretical Physics
Gonit Sora
Arxiv.CO
Arxiv.NT
Arxiv.GM
Ron Graham Archives
Krishnaswami Alladi
George E. Andrews
Arvind Ayyer
Rupam Barman
Nayandeep Deka Baruah
Roger Behrend
Bruce C. Berndt
Gaurav Bhatnagar
Shane Chern
Mihai Ciucu
Bishal Deb
Ilse Fischer
Ankush Goswami
Christian Krattenthaler
Tri Lai
Jeremy Lovejoy
Bibekananda Maji
Pankaj Jyoti Mahanta
Anupam Saikia
Michael Schlosser
Florian Schreier-Aigner
James A. Sellers
Fernando Rodriguez Villegas
Khimpi Dutta
Terence Tao
Tim Gowers
Onionesque Reality
Tanya Khovanova
The Aperiodical
Math with Bad Drawings
The value of the variable: H. A. Helfgott
Luit-Pariya
Gil Kalai
Peter Cameron
Igor Pak
British Combinatorial Committee
Kaneenika Sinha
Academia Obscura
Pankaj Jyoti Mahanta
Viviane Pons
Mukunth V
Integers
Bulletin of the Australian Mathematical Society
The Electronic Journal of Combinatorics
Journal of Integer Sequences
Journal of Number Theory
The Ramanujan Journal
The Mathematical Intelligencer
Annals of Combinatorics
Discrete Mathematics
European Journal of Combinatorics
The Journal of Irreproducible Results
Annals of Improbable Research
Proceedings of the National Institute of Science
Journal of Universal Rejection