How does glucose uptake happen in the various tissues of the body?
As far as I am aware, all tissues have glucose transporters, but there are many different types with varying tissue distribution. A short review in Biophysical Reviews (2016) by Navale and Paranjapei is freely available and provides a summary with links to original papers.
In short, there are two types of glucose transporter, those involving sodium symport (SGLTs) and those operating by facilitative diffusion (GLUTs). The review lists six SGLTs and mentions thirteen GLUTs, belonging to three different structural classes.
The tissues specifically mentioned in relation to one or more of these transporters include:
For SGLTs — small intestinal cells, proximal tubule of nephron, intestine, testes, uterus, lung, brain, thyroid, kidney, liver, uterus, pancreas.
For GLUTs — pancreatic beta cells, liver, kidney, brain, heart, skeletal muscle, adipose tissue, small intestine, testes, placenta.
I reproduce below a table from Chapter 6, Insulin and Sugars, in Gerald Litwack
Human Biochemistry (2018). The chapter is available if you belong to an institution with a subscription to Springer publications.