Differences between 推荐 and 建议
推荐 = recommend (closer to push for)
建议 = suggest (closer to advice)
If you know the difference between 'recommend' and  'suggest' you should have no difficulty deciding when to use which.
推荐 applies to objects; 建议 applies to actions
Example:
推荐某人当顾问 (O)
建议某人当顾问 (X)
建议让某人当顾问 (O)
沒人推荐他 (O)
沒人建议他 (X)
沒人建议用他 (O)
孔明向刘备推荐联吳抗曹 (X)
孔明向刘备推荐联吳抗曹的策略 (O)
孔明向刘备建议联吳抗曹 (O)
孔明向刘备建议联吳抗曹的策略 (?) - 建议策略 clearly implies 建议(實行)策略, therefore omitting the verb 實行 is acceptable
孔明向刘备建议實行联吳抗曹的策略 (O)