Is this about a life on a 2D hyperplane or a sphere in a hyperbolic 3D space (the question mentions both)? The life will be drastically different in these two cases. Note that curvature $\frac{1}{9}m^{-2}$ is kind of extreme. I assume the spacetime is a "hybrid" of hyperbolic 2D (or 3D) space and absolute Newtonian Euclidean time (if the time is hyperbolic as well, we get anti-de Sitter space which means geodesics (worldlines of two points in rest) will diverge and you get quite a good model of a rapidly expanding universe - your planet will have rather short life!)
First, the Sun - 100 million miles, let's say $160\cdot 10^{9} m$ means the light (and gravity) is reduced by $sinh^2 \frac{160\cdot 10^{9}m}{3m} \approx \frac{1}{2}e^{2\cdot 5\cdot 10^{10}} \approx10^{2\cdot 10^{10}}$... just forget about it, there is no way to even compare it with anything (and literally anything, like shining a match across observable universe is immensely brighter) from our universe.
The vision will also work with an exponential decay - say you see object up to 10km in Euclidean space. Then in the hyperbolic space you'll see objects up to 20m.... (note however that's a lot of space in there)
2D hyperplane
Let's assume the area you are interested in is that of a very small country, say inside a circle of 100km radius (approx. $30000 km^2$. In the hyperplane, the country is inside a circle with radius a bit over 60m... 319
So your map has to depict a circle with 60m radius and the area of $30000 km^2$. Or, in 1:1000 ratio, your map will have to display 6cm circle with an area of $30000 m^2$. I guess any "map" will be purely topological, displaying (or even only describing) major terrain features, more in terms of very precise angles (in hi tech society) from other terrain features - like "10 m from the tower in the azimuth 12°10'12.57664'' there is a well". Note that all topographical features will be necessarily rather small in their diameter.
For sufficiently technological civilization, use radio beacons. Since the world has much less distance per surface area compared to Euclidean one, beacons should be more or less receivable even if the signal decays exponentially, especially if the transmitters use directional beams. Then it's just a variant of fox hunting. Even a form of GPS is possible with triangulation and sufficient computational resources.
3D hyperbolic space, spherical planet
A sphere in hyperbolic space is a sphere, with a positive (2D) surface curvature.... so nothing different from mapmaking of Earth surface.
The problem is that with the space curvature radius 3m, standing on the surface of the planet will look like standing on a very steep hill, rapidly disappearing into the infinite abyss below (remember vision works very differently). So map will be inherently more navigable than the reality.
(also, the planet with Earth surface will have a radius of about 40m)
EDIT: it's a hyperplane & add radio beacons 204