stats.espncricinfo.com
In the course of ODI history, between top 8 sides, India has seen batsmen average 33.81 rpw @ 5.22 RPO. It is the highest average for a top 8 host nation. Australia has seen batsmen average 28.75 @ 4.62.
This might be a little misleading because more games were played in Australia in the early days (pre 1990).
Running the same query again, with a date filter shows:
stats.espncricinfo.com
India are still the top nation for batsmen who average 34.31 @ 5.33 RPO. Sri Lanka is the worst country for batsmen who average 29.35 @ 4.86 RPO. Australia comes a close second at 29.67 @ 4.81 RPO. India has the highest RPO and Australia has the lowest RPO in that time.
If only away or neutral games are looked at, India is still the fastest country to score runs in and Australia is the slowest. However, foreign batters average slightly more in Pakistan and the West Indies than they do in India, suggesting that Indian batsman are significantly better in India than foreigners.
If you look at home averages, New Zealand and the West Indies are at the bottom of the list, while India and South Africa top it (confirming again that India gives its batsmen a significant home advantage). Win loss ratios favour South Africa and Australia, who both have a win/loss ratio of over 2 at home. India come in third. Pakistan and the West Indies are at the bottom of that list, having the worst home records (though this doesn't take into account the UAE for Pakistan).
In tests, it's taken for granted that the pitches make a difference to batsmen and their ability to play. In ODIs, the pitches are more homogenous but there is still some statistically significant variability between countries (and, more specifically, individual grounds).
stats.espncricinfo.com
On a ground by ground basis, the top 3 grounds for batting averages are all in India. All 6 major Australian venues are jammed between the top 2 and bottom 2 New Zealand venues for averages. Things look pretty similar when looking at run rates too.