If you have one week to spend in Basingstoke and Deane, you could visit:
The Vyne - a beautiful Tudor estate with a mansion, gardens and woodland walks. Allow at least half a day to explore.
The Milestones Museum - an indoor museum showcasing the history of Hampshire. You can easily spend a full day here.
Basing House - the ruins of a 16th-century Tudor mansion. Allow a couple of hours to explore.
Highclere Castle - the filming location for Downton Abbey, with stunning gardens and a fascinating history. Allow a full day to explore.
The Bombay Sapphire Distillery - a unique experience exploring the history of gin-making. Allow half a day for the tour and tastings.
As for places to stay, you could try:
The Hampshire Court Hotel - a modern hotel with spa facilities and good transport links.
The Wheatsheaf Hotel - a 17th-century coaching inn with comfortable rooms and great food.
The Red Lion Hotel - a historic hotel in the heart of Basingstoke with a friendly atmosphere.