Hi. I think what more important is the purity of your RNA and its stability. If you are about to do gene expression analysis, the mRNA needs to be subjected to the qRT-PCR reactions as soon as possible after you lyse your cells. Otherwise, you may store it in -20oC fridge. 

As for checking the purity, you may check the presence of other peaks at regions other than around 260 nm. Certain ratio of absorbance at 260 nm/280 nm has been shown to be a good indicator of purity of RNA/DNA. Somebody has asked the same question and I saw great answers there. 

Good luck.

https://www.researchgate.net/post/I_am_checking_DNA_RNA_conc_purity_in_nano_drop_for_purity_I_am_seeing_a_peak_at_260_280_nm_what_does_it_confer_Peaks_are_also_coming_at_other_nm

I agree with Kemas, the ratios on your nanodrop output are important. You have plenty of total RNA for expression studies (qPCR). Just ensure that your 260/280 and 260/230 ratios for all your tissue samples are both acceptable and similar to each other. For pure RNA, your 260/280 should be 2.0 and 260/230 should be above 2.0 usually this is in the range of 2.0-2.30

Have you performed a DNase I digest? The Nanodrop will also be measuring DNA as part of the total yield. The amount of DNA present will depend on the extraction method - but without a specific DNase step it will be present

I think 1000ng/uL is too high. Samples definitely have DNA contamination. I will suggest you to check DNA contamination by normal PCR using some general primers. so that you can come to know if u have any DNA contamination. If you have DNA contamination do DNAase treatment again. Can you please share 260/280 ratio? if you checked concentration by Nanodrop.

260/280 was 2.1 and so as 230/260 showing perfect purity. But my concern was the very high concentration as I had earlier stated.

First of all, what is your final volume? Because if you have a concentration of 1000ng/ul with just 2ul, than it may not be too much. Also, what quantity of material you started with for extracting? Do you agree with me that if you used 50g of tomato leaves, 1000ng/ul would be plausible and maybe even less then expected?

May be your starting material was more and your elution volume was less leading to highly concentrated RNA. You should not worry until your RNA is pure and not degraded. You can dilute it further according to the experimental need. Just run the RNA on Agrose gel and see if u get 2 or 3 sharp intact bands for 28S, 18S and 5S (u may not see 5S band always). If you see a band sticking to wells, then it may be contaimnted by genomic DNA but looking at 260/280 ratio, its highly unlikely. 

Best.