What density does it take to go outside on a bright sunny day and look like someone that does not have thinning hair?

Grafts density is more or less  strategic , and much more dependent on candidate's  variable like grafts availability, grade of baldness , Candidate 's expectation and objective, potential hair loss of non transplanted area.
As a thumbs rule ,hair line and forelock area are made with approx  40-45 per sq cm 
mid scalp > 25-30 grafts per sq cm
Vertex Area> 40 grafts Per sq cm.
Grafts density allocation in hair transplants is based on  followed  principles:
1.  Hair grafts are limited resource and are not regenerated.  Higher density might lead to  constrained resourced for future need. That s why an optimal approach should be applied in graft utilization.
2.  Higher density above 50 might lead to tissue Necrosis and failed transplant result.
3.  A Hair Transplant  candidate is  futuristic entity,. The first transplant must not consume a high number of grafts to meet the the high density expectation, rather  preserving a reasonable number , if hair loss progresses further.

The density of grafts to give you enough coverage with a medium-coarse brown hair is probably 35% of your original density, something reasonable in a single hair transplant surgery